“That beats out the economy. That beats it all out to me, it’s not even close,” Mr. Trump said of the immigration issue, after playing the video on Tuesday night. “The United States is now an occupied country. But on Nov. 5, 2024, that will be liberation day in America.”

In the final weeks of a campaign that the former president has been waging more or less since his first year out of office, Mr. Trump is going with his gut, doubling down on the rhetoric that he believes won him the 2016 election and using immigration and the border to form the core of his closing message to voters.

Those instincts are at odds with the data, and with some of his advisers.

Mr. Trump has told aides that he beat Hillary Clinton in 2016 with the border but that in 2020 the border was “fixed” — illegal crossings had dropped to a dramatic low in part because of the coronavirus pandemic — so he could not use it as an issue against Joseph R. Biden Jr. He thinks immigration is more potent than ever as a political message, after the record levels of border crossings under the Biden-Harris administration and after he helped kill a bipartisan border security bill that the administration tried to pass.

But neither public nor private surveys support Mr. Trump’s theory of the race. Voters frequently rank the economy and the high cost of living as their most important issue.

Mr. Trump has spent considerable time and energy in recent days at economy-themed events, pitching proposals to make car loan interest fully tax deductible and to offer companies tax breaks and other benefits if they move their manufacturing to the United States or keep it there.

But Mr. Trump draws his energy from his rallies, and it is the reaction on immigration he is getting there that is helping convince him that the issue is better for him than the economy. When he launches into an immigration tirade, Mr. Trump gets animated, florid, dark and tribal. And there is a difference in how the audience and the press responds, compared with the response he gets when he talks about grocery prices, taxes or tariffs. It gets more attention, and it always has.

Mr. Trump has told allies that he thinks crowds get “bored” when he talks too much about the economy, according to a person close to him.

And Mr. Trump has a new reason for focusing on the issue: He has told rally audiences and people close to him that his opposition to illegal immigration saved his life.

In Butler, Pa., in July, Mr. Trump turned his head to look at a chart of illegal border crossings on a screen at the very moment a would-be assassin’s bullet missed his skull by less than an inch and grazed his ear. He has given the chart, and the issue it illustrated, an almost mythical status. “If you think about it, illegal immigration saved my life — I’m the only one,” Mr. Trump told a crowd in Aurora, Colo. “Usually, it’s the opposite.”

Some in Mr. Trump’s orbit, like his influential adviser Stephen Miller, fully support his instinct to emphasize immigration as the top issue for voters. Other allies worry that some of his more extreme immigration rhetoric — like his baseless claim that Haitian migrants are eating cats and dogs — risks turning off moderate voters whose support he needs.

Mr. Trump has been pushing advisers to get more immigration content, and they are obliging. Mr. Miller — the hardest of immigration hard-liners — has been flying more often on Mr. Trump’s plane since the summer and playing a big role in shaping his closing message. Mr. Miller declined to comment for this article.

Last month, Mr. Trump was intent on visiting Springfield, Ohio, after spreading unfounded rumors that Haitian migrants there were eating the pets of the city’s residents. He declared publicly that he would soon travel to Springfield.

Ohio is not considered a battleground state, but Mr. Trump thought it would be politically powerful to show up to highlight the perils of undocumented immigration. (The immigrants in question were in the country legally, including many who qualified for Temporary Protected Status after fleeing violence and chaos in Haiti.) But after bomb threats closed Springfield schools and threats against Haitians spiked, local Republican officials pleaded with Mr. Trump to stay away to avoid bringing further chaos to a city already under severe strain. Ohio’s Republican governor, Mike DeWine, added his voice, condemning Mr. Trump for smearing hardworking Haitians.

Many on Mr. Trump’s team privately thought that a visit to Springfield could do more political harm than good. At a Univision town hall broadcast on Wednesday, Mr. Trump continued to insist that he would visit Springfield. But no date has been announced.

Instead of going to Springfield, the compromise within the former president’s campaign was for Mr. Trump to give the speech in Aurora, Colo., a city he has used to exaggerate the harms inflicted by migrant gangs. Like Ohio, Colorado is not a battleground state, but Mr. Trump was determined to make the visit to highlight his personal top issue.

Speaking there on Oct. 11, Mr. Trump highlighted his desire to use the Alien Enemies Act — last used during World War II to place people of Japanese descent, among others, in interment camps — to deport gang leaders. The law lets officials make sweeping deportations of people from countries that have invaded or are at war with the United States, or that have made “predatory incursions.” While the Supreme Court has upheld past uses of the law, it is not clear whether the justices would allow a president to stretch it to encompass drug cartel activity as opposed to the actions of a foreign government.

Even when Mr. Trump does talk about the economy he tends to bring his points back to immigration. When The New York Times asked the Trump campaign for its plan to lower the cost of housing, the campaign’s response was that mass deportations would increase the supply of housing and therefore reduce costs.

Asked to explain Mr. Trump’s focus in the closing days of the race, a Trump spokesman, Brian Hughes, said: “President Trump rightfully recognizes that Kamala Harris’s porous border is at the heart of so many issues, whether it is high housing prices, low wages or overwhelmed hospitals and schools. An open border means that taxpayer dollars are wasted on illegal immigrants, instead of benefiting citizens. President Trump’s closing message is all about putting Americans first and restoring prosperity.”

Chuck Rocha, a Democratic strategist who has looked extensively at voting patterns, said Mr. Trump was taking a gamble that playing to fear would win him more votes than it costs him. He said some of Mr. Trump’s rhetoric might appeal to white suburban women troubled by the end of Roe v. Wade but also fearful of the influx of migrants, while at the same time possibly turning off other voters.

“He’s got a calculated risk option,” Mr. Rocha said.

Mr. Trump’s views on immigration, and the country’s, have evolved over time.

Immigration was not an issue Mr. Trump lingered on in 2011 when he considered running for president. Three years later, as illegal border crossings of unaccompanied children increased under President Barack Obama, the issue dominated conservative news media and became a focal point of Mr. Trump’s kickoff campaign speech in June 2015.

Now, immigration is a powerful motivating issue in a general election, the second-most important for many voters. And one of Mr. Trump’s signature policy proposals — building a border wall — is now broadly popular, expanding beyond Mr. Trump’s base.

Mr. Trump already dominates among the voters who care most about immigration, so it remains unclear how much room he has to grow his vote share by hammering on the issue.

Voters have very clearly and steadily ranked the economy as their top issue this election, far ahead of abortion and immigration. Even Republicans were nearly twice as likely to list the economy as the most important issue to their vote over immigration in the latest New York Times/Siena College poll.

Mr. Trump is favored over Vice President Kamala Harris on both the economy and immigration. But while Mr. Trump’s lead on the economy has narrowed in some polls, his lead on immigration remains wide and consistent.

As he has pummeled Democrats for the influx of migrants, Ms. Harris and President Biden have scrambled to rebrand themselves as tough on immigration, including by pushing Mexico to step up its own enforcement to keep migrants from reaching the U.S. border. Ms. Harris was pressed on Wednesday on her positions on immigration in an interview with the Fox News host Bret Baier. She conceded that there remained systemic problems.

Ms. Harris has also sought to use Mr. Trump’s opposition to the bipartisan border legislation to counter that the former president has no interest in solving the problems there and wants only to exploit it as a political issue.

In a speech last month in Wisconsin, Mr. Trump promised to “liberate” the state from an “invasion of murderers, rapists, hoodlums, drug dealers, thugs and vicious gang members.”

“Nothing can be as serious as this — because this gets down to the very fabric of our society,” he said. “Your way of life.”

Mr. Trump stressed the same point in Atlanta on Tuesday night.

“After years of building up other countries, we will protect our borders, defend our families and protect our American suburbs, cities and towns,” he declared.

In the final weeks of the campaign, Mr. Obama is hopscotching across battleground states to energize Democrats and urge persuadable voters to support Vice President Kamala Harris. Public polls show Ms. Harris trailing Mr. Trump in Arizona as she struggles to win Latino voters by the same margins that helped President Biden squeak out a 10,500-vote win in the state in 2020.

On Friday, Mr. Obama took up the Democratic attacks on Mr. Trump’s age and competence, criticizing him for his meandering rally speeches and mocking him for swaying along to music for 40 minutes to close out a town-hall event on Monday in Pennsylvania. He told voters that the Donald Trump of 2024 was an “older, loonier” version of the man who had run in 2016 and 2020.

“Have you seen him lately? You have no idea what he’s talking about,” Mr. Obama said. “You’d be worried if your grandpa was acting like this.”

The Trump campaign responded by saying that under the Biden administration, men and women across an array of races and ethnicities have faced “a terrible economy, an unprecedented border crisis and surging crime rates.”

The crowd in Tucson who cheered Mr. Obama on was a mix of longtime Democrats in vintage “Yes We Can” T-shirts and teenagers who had not been born when Mr. Obama was elected in 2008. Kierce Miller, 16, said she got out of class on Friday to attend the rally because she wanted to see the president who, as the family story goes, once held her as a baby.

Chris Warner, 18, who is studying sports business at Arizona State University, said he supported the C.H.I.P.S. Act signed by President Biden that provided $280 billion for semiconductor research and manufacturing. He said Mr. Trump had been unable to fulfill his main campaign pledge of building a border wall.

“Trump’s presidency was kind of overrated,” he said.

Tucson is home to the University of Arizona and a bastion for Arizona’s Democrats. It is a vital source of votes for the party to balance the overwhelmingly conservative voters in rural parts of the state. In 2020, President Biden won Tucson and surrounding Pima County by 20 points. But several people who attended the rally on Friday expressed anxiety over whether their neighbors would show up in the same numbers in November as Mr. Trump’s base.

“I’m a little scared,” said Lisa Grijalva, 60, a city worker in Tucson. “It shouldn’t be this close.”

Ms. Grijalva said many of her neighbors in her largely Latino neighborhood are undocumented immigrants and young adults with protections under the Deferred Action for Childhood Arrivals program, and she worries they will be rounded up if Mr. Trump follows through on his plans for mass deportations.

Mr. Trump has intensified his nativist rhetoric in the closing stretch of the campaign, continuing to claim falsely that Venezuelan gangs have taken over Aurora, Colo., and blaming migrants for rampant crime and for taking American jobs. Surveys show that more voters trust Mr. Trump than Ms. Harris to handle the border. But the Democratic rallygoers in Tucson said his comments scapegoated Latinos and immigrants.

“They think we’re all criminals and rapists and drug dealers,” Ms. Grijalva said. “I’m tired of the nonsense and chaos.”

The former president made his comments about Jan. 6 and its aftermath at a time when, just weeks before Election Day, uncommitted voters in battleground states tell pollsters that among their top concerns is that they view him as a threat to democracy.

On Friday, on his website Truth Social, Mr. Trump amplified a conspiracy theory that the attack on the Capitol was staged by the federal government, and he promoted his false claims that widespread fraud cost him the 2020 election.

He reposted a meme that a user had originally posted on Thursday, which read: “January 6 will go down in history as the day the government staged a riot to cover up the fact that they certified a fraudulent election.” Those words appeared over two images of people swarming the outside of the Capitol building that day and waving American flags.

Earlier on Friday, on a podcast hosted by the conservative media figure Dan Bongino, Mr. Trump lamented how those arrested in connection with the attack have been treated.

“Why are they still being held?” Mr. Trump told Mr. Bongino. “Nobody’s ever been treated like this. Maybe the Japanese during the Second World War, frankly. They were held, too.”

During that war, people of Japanese descent were among those held in internment camps under the Alien Enemies Act of 1798, a law Mr. Trump has said he wants to try to use for mass deportations of undocumented immigrants if he returns to the White House.

A Trump campaign spokesman did not respond to an email seeking comment.

Voters mostly look back on Mr. Trump’s actions after the 2020 election as dangerous. Half of likely voters said his actions went so far as to threaten democracy, compared with 44 percent who said he was just exercising his right to contest the election, according to a New York Times/Siena College survey in July.

And in a recent survey from PRRI, a public opinion research firm, 53 percent of Americans — including 17 percent of Republicans — said Mr. Trump had broken the law to try to stay in power after the 2020 election.

And for undecided and persuadable voters in key battleground states that Mr. Trump is trying to win in the final stretch of the race, seeing him as a threat to democracy was among their top five concerns, with many specifically mentioning the events of Jan 6.

On Friday, Judge Tanya Chutkan, who is overseeing the federal case against Mr. Trump brought by the special counsel Jack Smith, unsealed a batch of records with extensive redactions. Mr. Trump’s lawyers have opposed the release of the information coming within weeks of Election Day.

Mr. Trump’s lawyers tried unsuccessfully to get Judge Chutkan to make prosecutors search for evidence of supposed undercover agents who were involved in the events of Jan. 6. She denied that request and wrote that Mr. Trump’s team had offered nothing more than “speculation” that such people existed.

Mr. Trump repeatedly offered a picture of the Capitol attack this week that downplays the violence that unfolded and maintains that he played no role in its buildup. Federal prosecutors have accused Mr. Trump of coordinating an effort to overturn his loss in the 2020 election, culminating in the violence that took place on Jan. 6 as Congress was certifying Joseph R. Biden Jr.’s win in the electoral college.

The violence was carried out by supporters of Mr. Trump, many of whom had attended a nearby rally where he spoke and told people to “peacefully” and “patriotically” walk to the Capitol. He had urged people to come to Washington for that rally, posting days earlier on social media, “Be there, will be wild!”

Mr. Trump told an undecided voter at a Univision town hall this week that his supporters swarmed Washington that day out of anger at the election.

“They thought the election was a rigged election, and that’s why they came,” Mr. Trump said at the town hall, adding falsely, “There were no guns down there. We didn’t have guns. The others had guns, but we didn’t have guns. And when I say ‘we,’ these are people that walk down, this was a tiny percentage of the overall, which nobody sees and nobody shows. But that was a day of love from the standpoint of the millions, it’s like hundreds of thousands.”

And at an event at the Chicago Economic Club this week, Mr. Trump said: “People were angry. People went there. And I’ll tell you what, they never show that, the primary scene in Washington was hundreds of thousands, the largest group of people I’ve ever spoken before, and I’ve spoken before, and it was love and peace. And some people went to the Capitol, and a lot of strange things happened there.”