After hours of speeches, Elon Musk, the leader of Space X, Tesla and X, introduced a surprise guest: Melania Trump, whose appearances on the campaign trail have been rare during her husband’s third presidential campaign. She spoke briefly before welcoming Mr. Trump to the stage.

He is wagering that the attention he will receive from his rally in the solidly blue state of New York, is worth a detour from critical battleground states, while Ms. Harris was focusing on Pennsylvania, one of the biggest swing-state prizes.

Vice President Kamala Harris was campaigning in Philadelphia on Sunday with several events, including at a Black church and a Puerto Rican restaurant. And she got support from the Puerto Rican superstar Bad Bunny, one of the biggest recording artists in the world and among the most influential Latino artists, who shared on Instagram various replays of a video featuring Ms. Harris making a pitch to Puerto Rican voters.

The second-to-last Sunday of the campaign opened with Ms. Harris and her rival’s running mate, Senator JD Vance of Ohio, making their case to national audiences on morning political shows.

Mr. Vance, in an interview on NBC News, said he agreed with Mr. Trump that Democrats like Representatives Adam Schiff and Nancy Pelosi posed a bigger threat to the United States than foreign adversaries. “I think what Donald Trump said was those folks pose a greater threat to the United States’ peace and security because America is strong enough to stand up to any foreign adversary,” he said, pointing to Democrats’ economic and immigration policies as bigger threats.

Ms. Harris, in a recorded interview with Norah O’Donnell of CBS, explained why she is choosing to deliver her closing argument speech at the Ellipse in Washington, D.C., on Tuesday — making the White House her televised backdrop. “I’m doing it there because I think it’s very important for the American people to see and think about who will be occupying that space on Jan. 20th,” she said. “This is a real scenario. It’s either going to be Donald Trump or it’s going to be me sitting behind the Resolute desk in the Oval Office.”

There are nine days left until Election Day. Here’s what else to know:

Harris’s closing argument: Future Forward, a super PAC supporting Ms. Harris, warned that attacking Mr. Trump as a fascist or questioning his character or stamina are less effective than highlighting Ms. Harris’s proposals.

Michelle Obama’s appeal: Rallying for the first time with Ms. Harris, the former first lady Michelle Obama delivered searing remarks on women’s health, and spoke about what she described as the life-or-death stakes of returning Mr. Trump to the White House. Read excerpts from Mrs. Obama’s speech.

Trump and Muslim voters: Mr. Trump celebrated endorsements from a handful of Muslim and Arab American leaders at a rally in State College, Pa., on Saturday, in a striking reversal from when, as president, he blocked travel from several predominantly Muslim countries. Even at moments during this campaign, he has drawn on the anti-Muslim sentiments from earlier in his political career. But Mr. Trump is hoping to pick up support from Muslim and Arab American voters as he tries to flip Michigan, a critical battleground that he lost in 2020.

Eric Adams rejects ‘fascist’: Mayor Eric Adams of New York said on Saturday that Mr. Trump should not be called a “fascist” or compared to Adolf Hitler, rejecting an argument from fellow Democrats in the final days of the campaign.

Nicholas Nehamas , Jazmine Ulloa , Maggie Astor and Neil Vigdor contributed reporting.

He and Ms. Ocasio-Cortez talked about the politics of Congress, where Mr. Walz served before he became governor and the Democrats’ vice-presidential nominee. They compared the House to “public school,” with the Senate being more like “private school.” The House, they agreed, is where policy for the nation is shaped, and Mr. Walz said he would have been proud to have voted for the Bipartisan Infrastructure Law, a signature achievement of President Biden’s administration.

As the talk turned to the Senate and its procedures, Mr. Walz said knowingly to Ms. Ocasio-Cortez: “I don’t know where you stand, but I’m going to guess you and I are probably the same on the filibuster.”

“Oh yeah, we have got to get rid of that thing,” Ms. Ocasio-Cortez responded.

Ms. Ocasio-Cortez was an early proponent of removing the filibuster several years ago. Vice President Kamala Harris said in September that she would support ending the filibuster to codify Roe v. Wade. After the stream ended, a Walz campaign official said that Mr. Walz “shares the vice president’s position.”

In their Bills-Vikings Madden matchup on Sunday, which Mr. Walz and Ms. Ocasio-Cortez played for just a scoreless first half, they discussed housing policy and she asked him about voters who might be frustrated by the huge sums of money in politics or by the Biden administration’s positions about the war in Gaza. Twitch showed that about 12,500 people were watching on Ms. Ocasio-Cortez’s channel.

“For people who are most frustrated, they need to see stuff getting done,” said Mr. Walz, who did not address the war in the Middle East directly.

They also discussed the importance of building coalitions. Ms. Harris’s presidential campaign has sought to draw Republicans turned off by former President Donald J. Trump, in addition to motivating core Democratic voters. The Twitch stream was part of a broader effort by the Harris campaign to reach men — and young men in particular.

“I do not think Governor Walz would have hopped on here if he didn’t value the power of the coalition we have here,” said Ms. Ocasio-Cortez, who has become an emissary to skeptical young progressives for the Harris team.

The stream ended with Mr. Walz showing Ms. Ocasio-Cortez a favorite game he plays on the Sega Dreamcast called Crazy Taxi. The name aptly described Mr. Walz’s driving style as he scrambled around as a taxi driver picking up fares while driving on the wrong side of the road.

“Is this how you drive in real life?” Ms. Ocasio-Cortez quipped.

Before they closed, Mr. Walz noted the unique nature of the moment.

“Do you think a vice president has gamed?” Mr. Walz asked. “I do not think Dan Quayle was gaming.”

Then Mr. Walz departed the stream and headed to a local Mexican restaurant to watch some real-life football. The Las Vegas Raiders were playing.

In an email circulated to Democrats about what messages have been most effective in its internal testing, Future Forward, the leading pro-Harris super PAC, said focusing on Mr. Trump’s character and the fascist label were less persuasive than other messages.

“Attacking Trump’s Fascism Is Not That Persuasive,” read one line in bold type in the email, which is known as Doppler and sent on a regular basis. “‘Trump Is Exhausted’ Isn’t Working,” read another.

The Doppler emails have been sent weekly for months — and more frequently of late — offering Democrats guidance on messaging and on the results of Future Forward’s extensive tests of clips and social media posts. The Doppler message on Friday urged Democrats to highlight Ms. Harris’s plans, especially economic proposals and her vows to focus on reproductive rights, portraying a contrast with Mr. Trump on those topics.

“Purely negative attacks on Trump’s character are less effective than contrast messages that include positive details about Kamala Harris’s plans to address the needs of everyday Americans,” the email read.

Chauncey McLean, the president of Future Forward, issued a rare statement to The New York Times downplaying the significance of the Doppler email.

“Don’t over-read this,” he said. “This is just one of our regular emails sharing testing results from thousands of pieces of earned and social media content. It shows people that the most effective way of using Trump’s words and behavior is tying them to consequences in voters’ lives. That’s what Kamala Harris does every day by comparing her to-do list with his enemies list, for example.”

Jennifer O’Malley Dillon, Ms. Harris’s campaign chair, said on Sunday on MSNBC that it has “real impact” that people close to Mr. Trump have spoken out against him.

“We know anecdotally, we know from our research, when someone like John Kelly stands up and speaks about what it was like to serve under Donald Trump, speaks about how he clearly wants unchecked power,” she said. “The American people are not comfortable with that.”

The Doppler email said Ms. Harris’s response to Mr. Kelly’s remarks during her town hall on CNN were only in “the 40th percentile on average for moving vote choice,” meaning it does less to push voters toward the vice president than other messages that scored higher. In contrast, a clip of Ms. Harris on Howard Stern’s program promising to expand Medicare to cover in-home care for the elderly tested in the 95th percentile, the email said.

Ms. Harris’s campaign did turn the audio of Mr. Kelly into a television ad but has spent relatively little on it so far.

In a public memo over the weekend, the Harris campaign signaled that her “economic message puts Trump on defense” and was likely to be a focus in the final week. “As voters make up their minds, they are getting to see a clear economic choice — hearing it directly from Vice President Harris herself, in her own words,” Ian Sams, a spokesman for Ms. Harris, wrote in the memo.

Ms. Harris is scheduled to deliver what her campaign has billed as a closing speech on Tuesday at the Ellipse in Washington — the same location where Mr. Trump rallied the crowd that eventually stormed the Capitol on Jan. 6, 2021.

Campaigns and super PACs cannot directly coordinate strategy so sending messages via emails such as Doppler is one way they can communicate via quasi-public channels.

But the email’s warning reflects an underlying split among Democrats about what constitutes an effective line of attack against Mr. Trump, and how to persuade the small group of uncommitted voters to cast ballots against someone whose aberrant political and governing behavior has become familiar to them over nine years.

Ms. Harris’s team had made it clear immediately after the Democratic National Convention that they planned to switch from the message that President Biden had used most, that Mr. Trump is a unique threat to the country. They argued that making Mr. Trump smaller in the minds of voters was crucial. In her convention speech, she called him an “unserious man” but warned that restoring him to power would have “extremely serious” consequences.

In the last few weeks, Ms. Harris’s message on the campaign trail has been more in keeping with Mr. Biden’s earlier warnings about Mr. Trump as an unstable opponent. “Unhinged, unstable, unchecked,” all appear on the screen of one recent Harris ad.

The Dopper email warned: “Focusing on Trump’s disturbing, ludicrous and outlandish behavior can be an effective lead-in to talking about substantive policy, but is not effective at moving vote choice on its own.”

Ms. Harris’s most-broadcast ad in the last week does that, beginning with a warning of Mr. Trump “ignoring all checks that rein in a president’s power” before shifting to grocery prices, Social Security, abortion and taxes.

But her campaign has spent more than $10 million on a 30- and 60-second ad in that period also focused on Mr. Trump’s “handpicked” advisers warning about him. “Take it from the people who knew him best,” the narrator says. “Donald Trump is too big a risk for America.”

The ad fared relatively poorly in Future Forward’s ad testing, according to results obtained by The New York Times and shared with Democratic allies. After voters were shown the ad, it moved the race between Ms. Harris and Mr. Trump by only 0.7 percentage points, where the most effective ads can shift the matchup by 2 percentage points.

Vendors did a brisk business in “Make America Great Again” ball caps. Members of a pro-Trump Jewish group threw arms around one another’s shoulders and sang a prayer in Hebrew. Some enthusiastic supporters predicted a red tsunami so huge that it could engulf even New York, where the former president trails in the polls by about 15 percentage points. Among likely voters in New York City, he is behind by 39 points.

Gregory Lamb, 27, from the Westchester County suburb of Mamaroneck, N.Y., and his father weaved through the thick crowd to get to the front of a “special guest” line. Mr. Lamb had gotten tickets through a campaign connection after volunteering to be a poll watcher.

“Kamala said during the debate that people don’t show up to Trump’s rallies, and that people are always bored and want to leave,” Mr. Lamb said. “I wanted to show her that we show up — and look how many people are around. We’re here and we’re not going anywhere.”

As the introductory speakers started inside the Garden, about 100 protesters assembled on the steps of Moynihan Train Hall across Eighth Avenue. Jennifer Fisher, 64, of Manhattan held up a sign with a photo of a 1939 pro-Hitler rally held at the Garden (which was then in another location).

She said she had a 93-year-old relative who had fled the Nazi regime in Austria through the Kindertransport program. “She told me one day she woke up, and half the world was crazy,” Ms. Fisher said. “That’s what it feels like now.”

Nadine Seiler, 59, held a sign that read, “Trump Should Be in Prison Now.” She had made it for a visit to New York in July, when Mr. Trump was initially scheduled to be sentenced after his felony convictions.

“This is New York City; there’s no way these people should outnumber us,” said Ms. Seiler, looking at the MAGA crowd.

The people in the pro-Trump crowd came from far and wide, arriving from Long Island and Queens and Staten Island and from as far away as Orlando, Fla.; Charleston, S.C.; and Arlington, Va. There was a large New Jersey contingent and some from Connecticut.

One supporter from New York City, Randy Ireland, 50, said he was often met with negative comments when he wore his MAGA hat in his neighborhood, Long Island City in Queens.

Mr. Ireland, an Air Force veteran, worries about the possibility of crime committed by recent migrants, some of whom stay in shelters near where he lives.

He mentioned the Venezuelan gang Tren de Aragua, which has made inroads in New York City and is one of Mr. Trump’s frequent talking points on illegal immigration. The police say gang members have been snatching cellphones and robbing high-end department stores.

Mr. Ireland expressed sympathy for migrants who come for a better life but said that regarding illegal immigration, “There needs to be some accountability in Washington for how it affects the rest of us.”

On a New Jersey Transit train rumbling up the Jersey Shore toward New York, Danielle Roman, 26, a nursing student headed to the rally, said that she believed Mr. Trump was a better advocate for women than Vice President Kamala Harris, including on abortion.

“He wants to leave it up to the states, which I agree with,” she said.

Some New Yorkers who had not heard about the event seemed mystified.

Adam Jackson, a bartender from the Bronx, stepped out of the subway and froze when he saw the throng of Trump fans filling the corner.

“It’s jarring,” said Mr. Jackson, 24. “Why? Why?”

Shortly after 3:30 p.m., big screens outside the Garden flashed bad news to those still waiting: The venue, which has an advertised capacity of 19,500 minus the space taken up by a production, was full.

For Dan and Richele Skarda of Woodbridge, N.J., who had been in line for an hour, the trip was still worth it.

“I got to see it, I got to feel it, I got to experience it,” said Mr. Skarda, 57.

Ms. Skarda added, “I’ve had more fun here now than I’ve had in forever.”

The couple planned to have dinner in the city, and Mr. Skarda suggested they find a motel in New Jersey. This would tide them over until their next date in two weeks: Iron Maiden at the Prudential Center in Newark.

“What he said, and I do agree with this, what he said is that the biggest threat we have in our country, it’s not a foreign adversary, because we can handle these guys,” he said. “We can handle foreign conflicts. We can’t handle — look, under Nancy Pelosi’s long life in public leadership, the United States has gone from the pre-eminent industrial power of the world to second next to China. That fundamentally belongs on Nancy Pelosi’s shoulders.”

And Mr. Vance, who appeared on Sunday morning news shows on CBS News, CNN and NBC News, sought to defend Mr. Trump against the recent warnings from several people who served in high-ranking roles in the Trump administration that the former president posed a threat to democracy.

John F. Kelly, the former Marine general who was Mr. Trump’s longest-serving chief of staff, said last week that Mr. Trump had praised Hitler and Hitler’s generals and met the definition of a fascist. And Gen. Mark A. Milley, the retired chairman of the Joint Chiefs of Staff, who was appointed by Mr. Trump, was quoted in Bob Woodward’s new book, “War,” calling Mr. Trump “fascist to the core.”

Mr. Vance sought to portray the former Trump administration officials who have criticized Mr. Trump as warmongers, or as bitter at having been fired.

And he downplayed the significance of Russia’s spreading disinformation in American elections, saying that it was bad but suggesting there was little the country could do about it.

On CNN, Mr. Vance was pressed on the threats that Mr. Trump has been making to political adversaries. Those threats include describing his opponents as an “enemy from within”; vowing to imprison people he deems to have “cheated” in elections, as he falsely accused Democrats and election officials of doing in 2020; and reposting calls on social media for specific Democrats and anti-Trump Republicans to be jailed or subjected to military tribunals.

“None of that sounds fascistic to you at all?” CNN’s Jake Tapper asked.

“No, of course it doesn’t,” Mr. Vance replied, denying that Mr. Trump had made some of the threats in question and saying that in other cases his words had been taken out of context.

All week long, famous people had been popping up on the campaign trail for Vice President Kamala Harris. There was Eminem in Michigan. James Taylor in North Carolina. Bruce Springsteen, Samuel L. Jackson, Tyler Perry and Spike Lee in Georgia. And, yes, Beyoncé, in Texas (Willie Nelson, too).

You had to wonder if some piece of Mr. Trump wasn’t at least a little jealous.

The celebrity equation is a complicated one for the former president. A former television star himself, he seems to crave the approval of famous people. But their contempt for him has its uses, too. Democrats use celebrity worship to motivate their base. Mr. Trump has celebrity hatred to motivate his.

To be famous is to be elite; to be a fervid Trump supporter is to hate and feel hated by elites everywhere.

The stampede of stars stumping for Ms. Harris in the final days of the presidential campaign just reinforced a grand narrative that Mr. Trump and his supporters tell themselves about the journey they are on together, in which they must take on all sorts of powerful forces arrayed against them. Movie stars and military generals, media personalities and musicians — it’s all one big cabal between Washington, New York and Hollywood. Beyoncé is the Deep State.

It’s a self-perpetuating cycle, a 10-year flame war between the entertainment world and Mr. Trump, whose most devoted supporters draw ever closer to him and farther from everything else. Their relationship with popular culture becomes predicated on its stance toward this one man. Some become increasingly alienated and angry as the list of A-listers they’re not supposed to like gets longer. Some grow defensive. They seek out new celebrities to call their own.

These tortured dynamics have played out powerfully in response to the celebrity mania on the campaign trail.

On Thursday, while Mr. Springsteen was opening for Ms. Harris in Atlanta, thousands of Mr. Trump’s supporters waited for him to appear at a college sports stadium in Las Vegas. Michael McDonald, the chairman of Nevada’s Republican Party, warmed up the audience. “Walking in here was fantastic,” he said, because he saw “so many celebrities — but they’re our celebrities.”

There was a performance by Common Kings, a reggae-rock band, and speeches by Vivek Ramaswamy and Tulsi Gabbard, who ran for president as a Democrat last time but recently became a Republican to support Mr. Trump.

Danica Patrick, the racecar driver, told the audience they ought to be proud to be Trump supporters, that they’re “an army of brilliant human beings” united in a fight against censorship. Gina Carano, the Trump-supporting actor who was dumped by Disney after she compared the experience of Jews during the Holocaust to the current U.S. political climate, spoke of her anguish at being blackballed by Hollywood. She railed against the town.

“A lot of celebrities say, ‘I’m leaving the country if someone I don’t like is installed in power,’” she said. “I plan on staying here and fighting it out. That’s what patriots do. That’s what the people who truly love Americans do.” The crowd erupted when she told them that Elon Musk, the richest person in the world and a recent convert to Trumpism, was funding her lawsuit against the Mouse House.

Mr. Trump’s supporters love that they can now count Mr. Musk — a true celebrity — as one of their own. They cheer at every mention of his name. Other stars hitting the trail for the former president this season are not quite as high-wattage: Dennis Quaid, Brett Favre, Kid Rock and Hulk Hogan. (Mel Gibson endorsed Mr. Trump this week, too).

Jack Posobiec, a right-wing conspiracy theorist, told the crowd that if Mr. Trump were to win, they would all be able to go back in time to “an America where a family can take their kids out to the drive-in under the stars” without worrying “that the movie would teach them to hate their country.” This was perhaps overly optimistic — would wresting back control of the executive branch also somehow put them in charge of the movie studios? — but the point was taken nonetheless. These Americans are not buying what Hollywood is selling. They clapped along.

Some were feeling tetchy about all the celebrities working against them. “All these people that have all this money that are up there talking to us about who we need to vote for, they don’t go to the grocery store, they don’t get their cars filled at the gas station,” said Kim Kinsman, a 65-year-old retiree from Las Vegas who had worked for a bakery company.

She said she would never watch another Julia Roberts movie again. Beyoncé, she said, “doesn’t know anything about anything.” What about Taylor Swift? “Worthless,” Ms. Kinsman said. “I agree,” added Heather Pelton, a 42-year-old Las Vegas homemaker who was standing nearby.

Other Trump supporters reasoned that the Democrats’ use of entertainers was a sign of weakness. Many of the famous faces boosting Ms. Harris are the same ones who tried and failed to get Hillary Clinton over the line in 2016. Ms. Harris “needs them more than ever,” said Sheila Mehrens, a 74-year-old retiree from Henderson, Nev. “She can’t get up and do something like Trump does,” Ms. Mehrens said, “so she’s got Bruce Springsteen.”

Mr. Springsteen’s performance for Ms. Harris in Georgia was evidently on Mr. Trump’s mind as well. As soon as he took the stage in Las Vegas, he said, “In Georgia tonight, they say that Kamala has just absolutely bombed.” But Mr. Trump also admitted that he was curious to see the stars come out for her, almost in spite of himself. “In fact, I was going to watch it, I didn’t want to come out, I wanted to watch that first,” he said.

“Isn’t that terrible?”

That was not quite how things played out.

The resident declined to stop projecting the logo. In response, the town aimed bright spotlights at the tower to dim the political message, and began fining the resident $100 per day for violating its bylaws.

By last week, the resident had stopped beaming his pro-Trump message — but refused to sign an agreement pledging not to do it again. The town is still shining spotlights on the tower to prevent any more partisan displays.

Supporters of former President Donald J. Trump rallied at a local intersection last weekend in defense of the resident. Local officials said their efforts to keep the water tower free of political messaging had cost the town money and had resulted in a flurry of vulgar phone calls and emails from supporters of the resident.

“This is a deeply unfortunate and unnecessary situation that the town of Hanson and its residents and government officials did not ask to be placed in,” the town’s five-member governing board wrote in a statement last week. Town officials did not respond to written questions from The Times, including about how much the town is spending on the spotlights.

The town has not publicly identified the resident. A copy of a cease-and-desist order in the matter that has circulated online named the resident, but The Times could not verify the person’s identity. The order also listed an address, but a person at that house declined to speak to The Times about the dispute.

Hanson, which has about 10,000 residents, is among the most politically divided places in Massachusetts. While President Biden easily defeated Mr. Trump in the state in 2020, winning 66 percent of the vote, Mr. Trump eked out a narrow victory in Hanson with 3,314 votes, compared with 3,244 for Mr. Biden.

Just after sunset on Thursday, the onion-shaped bulb of the water tower glowed brightly against the darkening sky, lit up by several sets of high-powered lights that town workers had arranged around its base. The tower’s surface was a blank slate, bearing no hint of a political message. The drone of generators powering the lights drowned out the chirp of crickets.

At the house listed on the cease-and-desist order, a man who spoke to The Times through a speaker near the door declined to say whether he had projected the sign or answer questions about the conflict.

On the house’s lawn, alongside several small Trump signs, was a large cutout image of the water tower illuminated by the Trump logo.

While social media lit up with debate about Hanson’s “Trump Tower,” most residents approached by The Times in recent days declined to voice opinions on the dispute.

Mark Vess, 73, who lives near the water tower, said on Saturday that he could not comprehend why the town was continuing to shine the spotlights — “subjecting neighbors to the incessant roar of industrial generators from dusk to dawn” — when his neighbor had stopped projecting the Trump sign more than a week ago.

“I’ve heard very few people say, ‘Oh gee, that guy might light the tower up again. The town should keep spending thousands of dollars in case he turns it back on,’” said Mr. Vess, a lifelong resident of Hanson who is retired. “They’re making fools of themselves.”

His support for his neighbor notwithstanding, Mr. Vess said that he found Mr. Trump “reprehensible,” and that he planned to vote for Vice President Kamala Harris.

Felony convictions? Reconcilable differences, it seems, for one evening anyway.

On Sunday, Mr. Trump is bringing his presidential campaign to Madison Square Garden, the brashest stop in a final election stretch that has showcased the race-baiting, bravado and grievance-soaked distortions that defined much of his New York life and have only been amplified since he left.

The appearance is a remarkable gambit even by his standards — a show of force at “the world’s most famous arena,” to use the venue’s own Trumpian superlative.

More than anything, though, it is a reminder, a provocation, a warning: New York will never be rid of him entirely.

And he will never be done with New York.

“To him,” said George Arzt, a veteran of city politics who first met Mr. Trump in the 1970s, “this is a conquest.”

If recent years have doubled as a series of faceoffs between the former president and his former city — the voters versus Mr. Trump, the local politicians versus Mr. Trump, The People v. Mr. Trump — this election stands as perhaps the eternal tiebreaker.

Mr. Trump’s defeat would not end his winding arc with New York, but it would make it easier for the city to banish him from thought at least occasionally.

His victory, by contrast, would position him once more as the vengeance-seeking specter idling above the skyline, a keeper of federal dollars that the city needs and of mental ledgers that he would never wipe clean as president.

“I have been treated very badly by the political leaders of both the city and state,” Mr. Trump said in 2019, announcing himself a permanent resident of Florida (primarily for tax reasons, people close to him say). “I hated having to make this decision, but in the end it will be best for all concerned.”

For much of Mr. Trump’s pre-presidency life, his social calendar could read as a guided tour of estimable New York landmarks.

He watched Yankees games from George Steinbrenner’s box. He swaggered among the famous and infamous at the East 68th Street townhouse where his lawyer, Roy Cohn, resided and presided. He owned the Plaza Hotel, put his first wife in charge of renovations and later married his second wife there.

For Mr. Trump, whose sensibility can still be suspended in his greed-is-good heyday, latent affection for a bygone New York has persisted.

“Still in his blood,” said Andrew Stein, a friend of Mr. Trump’s and a former New York City Council president.

But on matters of his hometown, that blood has mostly boiled for some time.

He has lashed out at Letitia James, the state attorney general, over a more than $450 million civil fraud judgment against him. He has thrashed Alvin Bragg, the Manhattan district attorney, over the 34 felony convictions in his hush-money case, looking miserable through much of the trial, which compelled Mr. Trump to spend more time in the city than he had in years.

Still, relations with some prominent New Yorkers seem to have thawed. Far from being roundly rejected by the city’s elite, Mr. Trump has coaxed support from several major business figures, like the investor Paul Singer, a previous holdout.

He has even found common cause with the beleaguered mayor, Eric Adams, since Mr. Adams’s federal indictment, saying without evidence that he, too, had been “persecuted by the D.O.J. for speaking out against open borders.” (Despite a past endorsement of Vice President Kamala Harris, a fellow Democrat, Mr. Adams has been conspicuously disinclined to distance himself from Mr. Trump’s gestures of solidarity.)

While Mr. Trump has said he plans to compete in New York — and some polling has suggested a closer race than in his past campaigns — Democrats have dismissed his event as an exercise in hubris.

They have also invoked a 1939 pro-Nazi rally at the old Madison Square Garden while pointing out that Mr. Trump’s former White House chief of staff, John F. Kelly, said that Mr. Trump meets the definition of a fascist and had repeatedly praised Adolf Hitler. (Mr. Trump’s team has condemned the rally comparison and Mr. Kelly. Mr. Trump told Fox News that he was “just the opposite” of Hitler.)

Despite its reputation for big-city liberalism, New York is hardly Republican-free. Before 2014, the city went two decades without a Democrat leading City Hall. Several pockets, especially across Staten Island, are exceedingly Trump-friendly.

In May, chants of “Build the wall!” filled a park in the Bronx for Mr. Trump’s first New York rally in eight years.

“Every athlete wants to play in front of their home crowd,” said Joseph Borelli, the Republican minority leader of the City Council.

And by now, there are few new experiences Mr. Trump seems interested in pursuing.

He has been an executive and played one on television. He has been president and would like to be again.

He has been a New Yorker and a lapsed New Yorker, at least until his mind wandered to a venue he had never filled — in a city that might never accept him but will, if he has his way, never escape him, either.

“This is a Queens boy,” Mr. Arzt said, “who thinks that if he comes to Manhattan, this is the world, and he’s conquering the world.”

“Do not put our lives in the hands of politicians, mostly men.”

“I want folks to understand the chilling effect, not just on critical abortion care, but on the entirety of women’s health — all of it. There are good reasons why so many women and physicians are horrified by what’s happened since Donald Trump’s justices overturned Roe v Wade. We’re seeing women scrambling across state lines to get the care they need.”

“This is real. So, do you think Donald Trump is thinking about the consequences for the millions of women who will be living in medical deserts? Does anyone think he has the emotional maturity and foresight to come up with a plan to protect us? Y’all, we are teetering on the edge.”

“And this will not just affect women, it will affect you and your sons. The devastating consequences of teen pregnancy won’t just be borne by young girls, but also by the young men who are the fathers. They, too, will have their dreams of going to college, their entire future is totally upended by an unwanted pregnancy.”

“I am asking you all from the core of my being to take our lives seriously. Please! Do not, do not put our lives in the hands of politicians, mostly men, who have no clue or do not care about what we as women are going through, who don’t fully grasp the broad reaching health implications that their misguided policies will have on our health outcomes. The only people who have standing to make these decisions are women with the advice of their doctors. We are the ones with the knowledge and experience to know what we need. So please, please do not hand our fates over to the likes of Trump, who knows nothing about us, who has shown deep contempt for us. Because a vote for him is a vote against us. Against our health. Against our worth.”

“What side of history do you want to be on?”

“And let me tell you all — to think that the men that we love to be either unaware or indifferent to our plight is simply heartbreaking. It is a sad statement about our value as women in this world. It is both a setback in our quest for equity, and a huge blow to our country standing as a world leader on issues of women’s health and gender equality. So fellas, before you cast your votes, ask yourselves, what side of history do you want to be on?”

“Now, I recognize that there are a lot of angry, disillusioned people out there, upset with the slow pace of change, and I get it. It is reasonable to be frustrated. We all know we have a lot more work to do in this country. But to anyone out there thinking about sitting out this election or voting for Donald Trump or a third-party candidate in protest because you’re fed up, let me warn you, your rage does not exist in a vacuum. If we don’t get this election right, your wife, your daughter, your mother, we as women will become collateral damage to your rage.”

“So, are you as men, prepared to look into the eyes of the women and children you love and tell them that you supported this assault on our safety? And to the women listening, we have every right to demand that the men in our lives do better by us. We have to use our voices to make these choices clear to the men that we love — our lives are worth more than their anger and disappointment. And we are more than just baby-making vessels.”

“If your wife is shivering and bleeding on the operating room table during a routine delivery gone bad, her pressure dropping as she loses more and more blood, or some unforeseen infection spreads and her doctors aren’t sure if they can act, you will be the one praying that it’s not too late,” Mrs. Obama said. “You will be the one pleading for somebody, anybody, to do something.”

And while she acknowledged the anger that many Americans feel about the “slow pace of change” in the country, she warned: “If we don’t get this election right, your wife, your daughter, your mother, we as women, will become collateral damage to your rage.”

Mrs. Obama’s words — at a rally in Michigan where she introduced Vice President Kamala Harris — amounted to an extraordinary centering of women’s bodies and their private experiences in an American presidential election. She discussed menstrual cramps and hot flashes, describing the shame and uncertainty girls and women feel about their bodies. She told women they should demand to be treated as more than “baby-making vessels.”

And she castigated the media and many voters for holding Ms. Harris to a higher standard than her opponent, for “choosing to ignore Donald Trump’s gross incompetence, while asking Kamala to dazzle us at every turn.”

“We expect her to be intelligent and articulate, to have a clear set of policies, to never show too much anger, to prove time and time again that she belongs,” Mrs. Obama said. “But for Trump, we expect nothing at all, no understanding of policy, no ability to put together a coherent argument, no honesty, no decency, no morals.”

The crowd roared in approval.

But it was her remarks on women’s health that most captivated the audience. Mrs. Obama told her audience that Mr. Trump would further damage women’s health care, while Ms. Harris has vowed to enshrine the protections of Roe v. Wade in federal law.

Those protections, Mrs. Obama said, went far beyond the right to an abortion, extending to the private and vital relationships women and girls have with their doctors.

Mrs. Obama’s message was, in part, a counterpoint to the argument her husband, former President Barack Obama, made to Black men earlier this month, when he sternly suggested that sexism might be preventing them from voting for a woman. Perhaps, Mrs. Obama seemed to say, men could instead be persuaded to vote for the women in their lives.

“I am asking you all, from the core of my being, to take our lives seriously,” she said.

With the election 10 days away, Ms. Harris is facing an electorate deeply divided by gender. A majority of women support her. A majority of men are backing Mr. Trump. Her joint appearance with Mrs. Obama in Michigan seemed designed both to energize her female supporters and jolt men into understanding what she believes is at risk.

Polls in the state, which she almost certainly must win to capture the White House, show a race that is essentially tied, as in the other battleground states and the nation at large. President Biden won Michigan in 2020 with strong support from its Black voters, as well as Arab Americans and Muslims. But Ms. Harris is not polling as well with Black voters, especially men, and many Arab Americans and Muslims say they will not vote for her because of the Biden administration’s support for Israel in the war in Gaza. (At one point on Saturday, Ms. Harris was interrupted by a man in the crowd shouting “No more Gaza war.”)

The Harris campaign has tried to draw the backing of other voting blocs, particularly moderate suburban women who have expressed dissatisfaction with Mr. Trump. Kalamazoo County, where she and Mrs. Obama spoke on Saturday, is a predominantly white slice of southwestern Michigan, home to many voters who chose former Gov. Nikki Haley of South Carolina over Mr. Trump in the state’s Republican primary.

On Saturday, speaking after Mrs. Obama, Ms. Harris made what has become her standard political pitch in reaching across the aisle to women concerned about abortion rights and their safety.

“We’re seeing women scrambling across state lines to get the care they need,” Ms. Harris said. “Do you think Donald Trump is thinking about the consequences for the millions of women who will be living in medical deserts?”

Mrs. Obama had made those stakes plain, in terms that are almost never raised in the spotlight of a national campaign.

“I want the men in the arena to bear with me on this, because there’s more at stake than just protecting a woman’s choice to give birth,” she said. “Sadly, we as women and girls have not been socialized to talk openly about our reproductive health. We’ve been taught instead to feel shame and to hide how our bodies work.”

Young girls might not know what to expect from puberty. Women “my age,” she noted, don’t know what to expect from menopause. Now, they face the erosion of their health care options, she said, in the wake of Dobbs, the Supreme Court’s ruling on abortion.

“Look, a woman’s body is complicated business, y’all,” Mrs. Obama said, to laughter. As she spoke, there were nods of agreement, incantations of “Yes,” from around the room.

“And in those terrifying moments when something goes wrong — which will happen at some point to the vast majority of women in this country — let me tell you, it feels like the floor falls out from under us,” she said. “In those moments, all we have to rely on is our medical system, in those dark moments, all we have to rely on is our faith in a higher power and the experience of doctors to get us the care we need in a timely manner.”

“And look, I don’t expect any man to fully grasp how vulnerable this makes us feel, to understand the complexities of our reproductive health experiences,” she said.

Mrs. Obama spoke at the Democratic National Convention in August but has not campaigned for Ms. Harris since. She has long expressed her dislike of the campaign trail, including on Saturday, when she said,“Y’all know I hate politics.”

But she remains one of the most popular and unifying figures in the Democratic Party.

In many ways, her joint appearance with Ms. Harris represented exactly the kind of generational and cultural change that the vice president has sought to emphasize in her breakneck campaign to defeat Mr. Trump.

After Ms. Harris finished speaking, Mrs. Obama strode back onstage. As the crowd watched, the nation’s first Black first lady tightly embraced its first Black vice president.

Erica L. Green contributed reporting.