The situation reflects the strange place Mr. Musk occupies in American politics: a multibillionaire whose companies are contracted to provide vital services to the U.S. government; the owner of a wide-reaching social media platform, on which he often rails against the inefficiencies of the federal government; and a vocal, active supporter of Mr. Trump’s presidential campaign.

It also reflects the inevitable politicization of natural disasters on the eve of a close-fought election.

On Monday afternoon, during a visit to Valdosta, Ga. — a city on the state’s southern edge that sustained substantial damage in the storm — Mr. Trump described the lack of internet connection and basic communications infrastructure in North Carolina.

“I just spoke to Elon,” Mr. Trump said. “We want to get Starlink hooked up, because they have no communication whatsoever. Elon will always come through, we know that.” He added, “We are going to try to get Starlink in there as soon as possible.”

At a campaign event in Milwaukee the next day, Mr. Trump again reflected on the damage and the communication blackout in parts of North Carolina and praised Mr. Musk’s speedy response.

When Mr. Trump’s remarks were first reported, Andrew Bates, a White House spokesman, corrected the record. “This is already happening,” Mr. Bates wrote on social media, linking to a news release from the Federal Emergency Management Agency from Saturday, which outlined emergency measures authorized by the Biden administration.

According to the release, 40 Starlink systems were already available for emergency responder communications, and an additional 140 were on the way. Starlink comes in the form of small terminals, about the size of a pizza box, that connect to low-orbit satellites. They have been used in natural disasters in the United States in recent years, a FEMA spokeswoman said; they have also been vital to the Ukrainian military during the Russian invasion.

Representatives for Mr. Musk, Mr. Trump’s campaign and SpaceX did not respond to requests for comment.

Late on Monday night, Mr. Musk wrote on X, the platform he owns, “Since the Hurricane Helene disaster, SpaceX has sent as many Starlink terminals as possible to help areas in need.” He added that earlier in the day, Mr. Trump had “alerted me to additional people who need Starlink Internet in North Carolina.”

“We are sending them terminals right away,” he wrote.

Since then, Mr. Musk has amplified posts, including by Starlink’s official X account, that detail efforts by private individuals and organizations to deliver Starlink systems to the state. On Wednesday, Ivanka Trump posted on social media that she had toured the damage of western North Carolina with a relief group that had also distributed more than 300 free Starlinks. (“Thank you, Elon!”)

The donated devices may come at no cost, but the free internet service is temporary. On the company’s website, Starlink said it would provide 30 days of service for the devices in affected areas, before a standard residential subscription would be charged.

As of Wednesday morning, FEMA had provided 67 Starlink systems to North Carolina, including three to the Eastern Band of Cherokee Indians and four “for critical lifeline locations as determined by the state,” according to Jaclyn Rothenberg, a FEMA spokeswoman.

Ms. Rothenberg said the agency was ordering hundreds more Starlink units.

The role of the federal government in the provision of Starlink services has gone unmentioned by Mr. Musk on social media — with one significant exception.

In a post on X Wednesday, Mr. Musk said the Federal Communications Commission had previously “illegally revoked” an award to SpaceX that would have provided Starlink kits that “probably would have saved lives in North Carolina.”

Mr. Musk’s post is misleading, however. The F.C.C. had a two-part approval process for its rural subsidies; while SpaceX won an initial bid, the agency decided in 2022 not to award it upon further review, according to an F.C.C. spokesman.

The agency found that Starlink had trouble meeting basic upload and download speeds and that rural subscribers would have had to pay an upfront fee of $600 at the time for a dish. The F.C.C. also said it had hit roadblocks getting more information from SpaceX.

“In this instance, the agency denied public funds to more than a dozen companies — not just Starlink — who did not meet the program requirements,” the spokesman said. The agency stands by its decision, he added.

Kirsten Grind contributed reporting.

On the Screen

Like most Trump campaign ads, this one opens with an stern-looking photo of Vice President Kamala Harris. Bold text appears on the screen beside her. It’s The New York Times logo, a mark of authority, over a fragment of a sentence from an article published on Aug. 22.

“Harris is seeking to significantly raise taxes,” reads the male narrator, underscored by ominous-sounding music.

A video — helpfully subtitled — shows Ms. Harris saying, “Taxes are gonna have to go up.” (It will be replayed seconds later.) No context is provided about whose taxes will have to go up. More unflattering photos appear of Ms. Harris bearing a pained expression, smiling alongside the unpopular President Biden, and seeming to smirk.

The ad closes by contrasting Ms. Harris unfavorably with her opponent. The tone of the music shifts from ominous to triumphant. Video shows Mr. Trump purposefully striding through a corridor in the Capitol as president, wearing a hard hat, touring a factory floor and shaking hands with fast-food workers. The narrator cites three of the most populist tax proposals from Mr. Trump’s 2024 campaign: “No taxes on tips, overtime or Social Security.”

The Script

Narrator

“Kamala Harris is gonna significantly raise taxes.”

Ms. harris

“Taxes are gonna have to go up.”

Narrator

“Kamala’s plan will raise families’ taxes by nearly $2,600 a year. Under Kamala, prices have already soared. Now, she’d make it worse with even higher taxes.”

Ms. harris

“Taxes are gonna have to go up.”

Narrator

“President Trump will cut taxes, again. No taxes on tips, overtime or Social Security.”

Accuracy

It’s no mystery why the Trump campaign chose to truncate a sentence from The Times’s Aug. 22 article on Ms. Harris’s tax plan. The full sentence would not have made for good advertising copy for the populist Trump campaign: “Harris is seeking to significantly raise taxes on the wealthiest Americans and large corporations.” (Italics added.)

Those missing words constitute the central deception of the ad, one that is repeated throughout. Middle-class viewers would come away from the ad with the strong impression that Ms. Harris planned to raise their taxes and that Mr. Trump wanted to cut them.

But that’s not true. While Ms. Harris said in 2019 that she wanted to scrap Mr. Trump’s tax-cut law, the aspects of the law that she criticized were the tax cuts for corporations and for the top 1 percent of earners. Ms. Harris has since promised — as President Biden did — that no American earning less than $400,000 a year would see their taxes go up under her presidency.

The Takeaway

The strategic imperative of the ad is clear.

Mr. Trump’s campaign is spending more money advertising on the economy than on any other issue for a simple reason: The campaign’s internal polling shows that the economy — and in particular, concerns about the higher cost of living — is by far the most important issue for the undecided voters they are targeting in the seven battleground states.

This ad zeroes in on taxes to drive home the campaign’s overall message that Ms. Harris’s policies would result in voters having less money in their pockets. The way Republicans see it, if they are arguing over taxes, they are winning. The Trump team plans to put millions of dollars behind this ad, according to Mr. Trump’s senior adviser Chris LaCivita.

Some Democratic strategists don’t see it that way; the Biden pollster John Anzalone has advised Democrats to lean into the issue of taxes on populist grounds, by pointing out that Republicans want to cut taxes for big businesses and the rich. And it’s telling that the Trump ad makes no mention of Mr. Trump’s huge tax cuts for corporations, the heart of his 2017 tax bill.

The immigrants in question are living and working in the United States legally through the Temporary Protected Status program, which Congress created in 1990 for people from countries experiencing war, natural disasters or other crises. The Department of Homeland Security designates countries for up to 18 months at a time based on the current conditions, and the designation can be renewed indefinitely.

Haiti was initially added in 2010, under President Barack Obama, after a 7.0-magnitude earthquake devastated the country. It has since experienced a major hurricane and a cholera epidemic.

“Absolutely I’d revoke it, and I’d bring them back to their country,” Mr. Trump said in an interview with NewsNation on Wednesday.

He spoke at length about Haitian immigrants living in Springfield, Ohio, claiming that the city had been a utopia — “you had a beautiful, safe community, everyone’s in love with everybody, everything was nice, it was like a picture community” — and that the Haitians had destroyed it.

Haitian immigrants in Springfield have been a primary target of Mr. Trump’s and Mr. Vance’s vitriol, including the debunked smear that they have killed and eaten pets. The city later faced a series of bomb threats that closed schools and government offices for days.

The mayor of Springfield and the governor of Ohio, both Republicans, rejected the Trump campaign’s characterizations, as has a local business owner and two-time Trump voter who employs Haitian workers and received death threats for defending them. The governor, Mike DeWine, wrote in an opinion essay in The New York Times last month that, while there had been “challenges” in accommodating thousands of new people, the immigrants had benefited Springfield economically.

As president, Mr. Trump sought to end the temporary protection for immigrants from Haiti, as well as those from El Salvador, Honduras, Nepal, Nicaragua and Sudan. Some of those decisions, including the attempt to revoke Haiti’s status, were challenged in two court cases during his administration: Saget v. Trump and Ramos v. Wolf.

There is no dispute that the executive branch has the authority to remove countries from the T.P.S. program. But the plaintiffs in both cases argued that the administration had not followed the appropriate procedures for doing so — namely, by assessing whether conditions in each country still justified protection — and that the administration’s decisions had been based on racial animus.

In both cases, district courts temporarily blocked the Trump administration from removing the protections. In the Ramos case, an appeals court reversed the district court in 2020, ruling that the removals could proceed, but the court later granted a request for further appeal. In the Saget case, an appeals court never ruled because the Biden administration’s decision to keep Haiti in the T.P.S. program made it moot.

Mr. Biden’s reversal of Mr. Trump’s decision meant the legal questions involved were not definitively resolved in either direction.

Geoff Pipoly, who was a lead attorney on the Saget case, said comments like Mr. Trump’s on Wednesday could form the basis for a new lawsuit if he were to try again to revoke Haitian immigrants’ status, because they would provide evidence that the removal was based on Mr. Trump’s desired outcome, rather than on an assessment of whether conditions in Haiti made it safe for people to return.

“This is supposed to be an evidence-based decision — what the T.P.S. statute requires is, is it safe for these people to return, and that requires a review of the conditions on the ground,” Mr. Pipoly said. “Reasonable minds can differ about what those country conditions mean. But what happened in 2017 was that you had the career officials saying it’s not safe to go back to Haiti, and you had elected officials saying: ‘Who cares? Do it.’”

She made her remarks in a promotional video for a new memoir scheduled for release on Tuesday. Her husband, who opposes federal abortion rights and has taken credit for helping overturn Roe v. Wade, did not immediately comment.

“Individual freedom is a fundamental principle that I safeguard,” she said in the video, which was posted to her account on X. “Without a doubt, there is no room for compromise when it comes to this essential right that all women possess from birth, individual freedom. What does ‘my body, my choice’ really mean?”

On Wednesday evening, The Guardian published excerpts from Mrs. Trump’s book, in which she went further than her words in the video: “A woman’s fundamental right of individual liberty, to her own life, grants her the authority to terminate her pregnancy if she wishes.”

She also defended some abortions performed in the later stages of pregnancy, mostly out of medical necessity or to save the life of the mother: “As a community, we should embrace these common-sense standards. Again, timing matters.” But she did not elaborate on which policies she would like to see enacted in a post-Roe landscape.

A spokeswoman for Skyhorse Publishing, the publisher of the book, did not respond to a request to confirm the book’s contents or supply an early copy.

One person close to Mr. Trump, who insisted on anonymity and was not authorized to speak publicly, said the campaign had been aware that the video was being released, but suggested that it was an attempt by Mrs. Trump to sell her book and not part of a coordinated effort to soften the former president’s image. The person noted that she and her husband do not always take the same views.

A spokesman for Mr. Trump’s campaign did not respond to an email seeking comment about how the candidate felt about Mrs. Trump discussing her views, or how her comments in the video comported with his false statement that both Democrats and Republicans wanted an end to Roe v. Wade.

Still, Mrs. Trump’s remarks align with a message his campaign has been trying to send in recent weeks: that the former president is not an ardent opponent of abortion rights. About one-third of Republicans support access to the procedure, along with a majority of independents. Her soft-focus approach may appeal to voters who have chosen what they want to glean from Mr. Trump’s kaleidoscopic views on abortion.

“This is a disgusting attempt to politicize an issue that has created so much undue suffering and even death in communities with abortion bans,” said Mini Timmaraju, the president of Reproductive Freedom for All, an abortion rights group. “Trump did this. I don’t think Melania cares about reproductive freedom; but if she does, where was she when he appointed the justices who overturned Roe, and unleashed the crisis we’re living in today? This is merely a desperate move from a desperate campaign to continue to do what they do best, lie to the American public.”

At the same time, Mrs. Trump’s comments have frustrated anti-abortion activists who believe that Mr. Trump would advance their cause and want to remain in good standing with him if he wins in November.

“The women of America are capable of great strength and creativity,” Marjorie Dannenfelser, the president of Susan B. Anthony Pro-Life America, pushed back cautiously on social media. “They are naturally inclined to speak for those who are powerless. Abortion is not the source of their freedom and liberation.”

The tension reveals the marked flip from the status anti-abortion activists enjoyed in October 2020, when Ivanka Trump declared in an interview days before the election, “I am pro-life, and unapologetically so.”

Mr. Trump is acutely aware of the political pressures he faces over abortion rights, but has been unable to figure out exactly what to say or where to land on specifics. He repeatedly boasts that he “terminated” Roe, yet wrote on his social media website after the Democratic National Convention in August that he would be great for “reproductive rights,” a phrase more associated with Planned Parenthood than with conservatives.

Since the Supreme Court overturned Roe in 2022, led by a conservative majority with three justices appointed by Mr. Trump, Republicans have toyed with the idea of a national abortion ban. Democrats, for their part, have won repeated electoral victories on the back of the issue, and voters even in red states have passed ballot measures to protect access to the procedure.

Now Democrats are seizing on abortion restrictions in Republican-led states — and the harrowing stories about women who died or faced life-threatening complications as a result — as a galvanizing issue ahead of November.

Mr. Trump has taken various positions on abortion rights over the years. In 1999, as he considered a presidential run as an independent, he called himself “very pro-choice.” A dozen years later, as he weighed running as a Republican, he changed his stance. “Just very briefly, I’m pro-life,” he told attendees at the Conservative Political Action Conference in 2011.

In the 2016 campaign, as he tried to figure out what he should say on the issue, he said women who had abortions should be subject to some form of punishment.

But since the overturning of Roe, he has waffled even more. In February, he privately told associates he liked the idea of a 16-week national ban, but wanted to wait until the primary race was over to say something.

He then reversed himself publicly in April, saying the issue should be left to the states, but he declined to say whether he would veto a national ban if one reached his desk as president. Despite saying states should decide for themselves, he has called Florida’s six-week ban a “terrible mistake” — but then, after more apparent vacillation, said he would vote against a ballot measure there that would expand the window for women to get abortions.

At Mr. Trump’s debate last month against Vice President Kamala Harris, he again declined to say whether he would veto a national ban on abortion, saying just this week for the first time that he would.

On Wednesday, in an all-capital-letters post on social media, Mr. Trump said: “Everyone knows I would not support a federal abortion ban, under any circumstances, and would, in fact, veto it, because it is up to the states to decide based on the will of their voters (the will of the people!).”

He went on to say he supported exceptions for abortion if a woman had been raped or was a victim of incest, or if her life was in danger.

Regardless of Mr. Trump’s personal beliefs, his administration pushed through the greatest restrictions on abortion rights in generations, not only appointing the justices who overturned Roe but also moving to restrict abortion access through executive actions.

Some Americans believe otherwise.

Even now, polling shows that nearly one in five voters in battleground states says that President Biden is responsible for ending a constitutional right to abortion. Trump supporters were even more likely to blame Democrats for the abortion bans.

Sarafina Chitika, a spokeswoman for Ms. Harris’s campaign, said in a statement that Mrs. Trump’s comments were at odds with her husband’s, and that Mr. Trump “has made it abundantly clear: If he wins in November, he will ban abortion nationwide, punish women and restrict women’s access to reproductive health care.”

During Mr. Trump’s 2016 campaign, Mrs. Trump told GQ magazine that she did not wade into politics: “Those policies are my husband’s job,” she said. As first lady, she did not discuss her views on abortion publicly or privately, according to two former administration officials who worked in her East Wing, one of whom insisted on anonymity to describe private conversations.

The other, Stephanie Grisham, a former White House press secretary and one of Mrs. Trump’s longest-serving aides during the administration, said that the issue never came up. Ms. Grisham, who has since released a memoir about her time working for the Trumps and spoke at the Democratic National Convention, did not see a master plan behind Mrs. Trump’s comments.

“I’m actually quite confused,” she said. ”At the end of the day, she’s trying to sell more books.”

Mrs. Trump has a long but inconsistent history of using her image to support Mr. Trump. In April 2011, she appeared on ABC’s “The View” to bolster her husband’s false claim that President Barack Obama had been born in Kenya, and his ensuing campaign that the president should release his birth certificate.

“It’s not only Donald who wants to see it,” Mrs. Trump said. “It’s American people who voted for him and who didn’t vote for him.”

In October 2016, Mrs. Trump went on television again to defend a leaked audio recording from “Access Hollywood” in which Mr. Trump bragged about grabbing women by the genitals. On CNN, she dismissed the comment as “boy talk” and suggested that the show’s former host, Billy Bush, had goaded Mr. Trump into saying “dirty and bad stuff.”

More recently, Mrs. Trump has declined to join her husband on the campaign trail. But she was paid $237,500 for an April speaking event with the Log Cabin Republicans, according to Mr. Trump’s 2024 financial disclosure form. The source of that payment is unclear.

Post-White House memoirs have long been a way for first ladies to express views they might have strategically muted to help their husbands politically. Between the book deal and the promotional tours, memoirs can also be cash cows.

Mrs. Trump’s representatives have taken an aggressive approach to promoting her book and soliciting money for her tour. CNN reported on Thursday that Skyhorse Publishing had asked the network to pay a $250,000 “licensing fee” in exchange for an interview with the former first lady. Paying for interviews is considered to be deeply unethical in many American newsrooms.

Skyhorse had sent the proposal alongside a nondisclosure agreement, which the network said it did not sign. Tony Lyons, the president and publisher of Skyhorse, later told CNN that the payment request was a mistake and that Mrs. Trump did not have knowledge of the arrangement.

A spokeswoman for Fox News, which has aired two recent interviews with Mrs. Trump, said on Thursday that the network had not paid for them.

Elizabeth Dias contributed reporting from Washington. Jack Begg contributed research.

The two women agree on little politically beyond their distaste for Mr. Trump. They had next to no relationship when they overlapped in Congress, though they did speak on the phone about Ms. Cheney’s endorsement earlier this summer.

The endorsement by Ms. Cheney — and that of her father, former Vice President Dick Cheney — is meant to show the breadth of Ms. Harris’s support, a point that her running mate, Gov. Tim Walz of Minnesota, made in his debate against Senator JD Vance of Ohio on Tuesday night.

“I’m as surprised as anybody of this coalition that Kamala Harris has built, from Bernie Sanders to Dick Cheney to Taylor Swift and a whole bunch of folks in between,” said Mr. Walz, name-checking the left-wing senator from Vermont and the world’s biggest pop music star. “And they don’t all agree on everything, but they are truly optimistic people.”

Ms. Cheney is a Wisconsin native who grew up in Virginia and represented Wyoming in Congress for six years. After Mr. Trump tried to overthrow the 2020 election results, she disowned him and participated in the House select committee investigating the Trump-inspired assault on the Capitol on Jan. 6, 2021. She so alienated fellow Wyoming Republicans that she was run out of office by a primary challenger loyal to Mr. Trump.

“As a conservative, as someone who believes in and cares about the Constitution, I have thought deeply about this and because of the danger that Donald Trump poses, not only am I not voting for Donald Trump, but I will be voting for Kamala Harris,” Ms. Cheney told an audience at Duke University in North Carolina last month.

Her appearance for Ms. Harris will be especially striking because of the timing: New evidence in the federal criminal case against Mr. Trump over his attempt to overturn the 2020 election became public on Wednesday in a 165-page brief from the special counsel, Jack Smith. In the final weeks of the presidential race, the details drew new attention to Mr. Trump’s actions surrounding Jan. 6 — a politically advantageous development for Ms. Harris at a time when the growing conflict in the Middle East and the dockworkers’ strike have become cause for concern.

Since becoming the Democratic nominee, Ms. Harris has tacked toward the center, trying to shed her reputation as a California liberal by repudiating many of the progressive positions she held when she ran for president in 2020.

This time around, she has described herself as a committed “capitalist,” laid out a hard-line position on border security and embraced fracking to extract natural gas from under Pennsylvania — a position she opposed during her first presidential campaign. Polls have shown that voters are more worried that Ms. Harris is too liberal than that Mr. Trump — who has proposed a series of radical right-wing policies — is too conservative.

Wisconsin is seen as a must-win state for Ms. Harris, along with Michigan, where she will campaign on Friday, and Pennsylvania, where she has appeared more than any other battleground. Ms. Harris has built a narrow lead in Wisconsin, rapidly recovering from President Biden’s deficit against Mr. Trump, according to a New York Times polling average.

A survey from Marquette Law School released Wednesday found that 71 percent of Wisconsin Democrats were enthusiastic about voting among in the presidential election — up from 40 percent in June, when Mr. Biden was still in the race.

Ms. Harris has also been endorsed by more than 100 former national security officials from Republican administrations and former Republican members of Congress.

Standing in front of a house covered in fallen trees in the Meadowbrook neighborhood of Augusta, Ga., Ms. Harris announced that the federal government would cover 100 percent of the costs of debris removal and other emergency protective measures for three months to help the state recover. She described how much of the community did not have power, with many lacking access to water, and how she had met one woman who lost her husband. She called the damage “extraordinary” and the loss of life “particularly devastating.”

Ms. Harris also met with local officials and received a briefing on recovery efforts, during which she praised emergency responders who were working even amid their own personal struggles, telling them she was “here to thank you and to listen.” She helped hand out food and snacks at a community center that had been turned into a shelter.

Her visit to the battleground state came as she has confronted an extraordinary confluence of political headwinds this week, including a widening conflict in the Middle East and a historic labor strike. The developments have forced her to balance the duties of being second-in-command while also projecting strength as the potential next commander in chief.

Ms. Harris’s visit to Georgia replaced plans for a campaign bus tour in Pennsylvania with her running mate, Gov. Tim Walz of Minnesota, who set off in the Northern battleground on his own the day after his vice-presidential debate. She will continue campaigning on Thursday in Wisconsin and Friday in Michigan, and is later set to travel to North Carolina to assess storm damage.

While Ms. Harris visited Georgia in her official capacity, the trip carried significance for her campaign. She is trying to repeat President Biden’s 2020 victory in the state, where polls show former President Donald J. Trump with a narrow edge. The race is also extremely close in North Carolina, which Mr. Biden visited on Wednesday and where the storm ravaged numerous communities, including the Democratic stronghold of Asheville.

After Helene struck, Mr. Trump moved quickly to capitalize, visiting Valdosta, Ga., on Monday and seeking to cast the natural disaster’s fallout as a failure of Ms. Harris’s and Mr. Biden’s leadership.

Both Democrats have been in touch with elected officials in the states hit by the storm, and have vowed to send as many resources as each place needs.

“We are here for the long haul,” Ms. Harris said in her remarks on Wednesday.

Mr. Biden signed disaster declarations for the affected areas, and the federal government has sent help, including more than 1,200 federal emergency personnel. On Tuesday, Mr. Biden also ordered the Department of Defense to deploy up to 1,000 active-duty troops to help deliver food, water and other services. He has also said that he expects to ask Congress for more relief funding.

But that has not stopped Mr. Trump and his campaign from accusing Mr. Biden and his administration of not being responsive to major emergencies. As the hurricane barreled down on the region over the weekend, the former president criticized Ms. Harris and Mr. Biden for being away from Washington.

“Biden is in Delaware sleeping right now in one of his many estates,” Mr. Trump, who owns more homes than the president, proclaimed at a rally in Pennsylvania. He said that Ms. Harris, who was attending fund-raising events on the West Coast, was “with her radical left lunatic donors, when big parts of our country have been devastated by that massive hurricane and are underwater, with many, many people dead.”

Mr. Trump’s knack for politicking off disasters has proved a vulnerability for the Biden administration.

In 2023, the former president visited East Palestine, Ohio, soon after a toxic train derailment saturated the town’s land with chemicals. It took Mr. Biden, who had promised to visit “at some point,” more than a year to arrive, to the dismay of many residents and even some elected officials in his own party.

During his trip to Valdosta on Monday, Mr. Trump falsely claimed that Mr. Biden had not been in touch with Gov. Brian Kemp of Georgia, which the governor, a Republican, promptly denied.

Wearing a red “Make America Great Again” cap, Mr. Trump concluded his remarks by saying, “We’re not talking about politics now.”