“As president,” the letter said, “he promoted daily chaos in government, praised our enemies and undermined our allies, politicized the military and disparaged our veterans, prioritized his personal interest above American interests and betrayed our values, democracy and this country’s founding documents.”

The letter condemned Mr. Trump’s incitement of the mob attack on the Capitol on Jan. 6, 2021, aimed at allowing him to hold onto power after losing an election, saying that “he has violated his oath of office and brought danger to our country.” It quoted Mr. Trump’s own former vice president, Mike Pence, who has said that “anyone who puts himself over the Constitution should never be president of the United States.”

The letter came not long after former Vice President Dick Cheney and his daughter, former Representative Liz Cheney of Wyoming, both said they would vote for Ms. Harris. Democrats featured a number of anti-Trump Republicans at their nominating convention last month, including former Representative Adam Kinzinger of Illinois. Mr. Pence has said he will not endorse Mr. Trump but has not endorsed Ms. Harris.

The 111 signatories included former officials who served under Ronald Reagan, George H.W. Bush or George W. Bush. Many of them had previously broken with Mr. Trump, including two former defense secretaries, Chuck Hagel and William S. Cohen; Robert B. Zoellick, a former president of the World Bank; the former C.I.A. directors Michael V. Hayden and William H. Webster; a former director of national intelligence, John D. Negroponte; and former Gov. William F. Weld of Massachusetts. Miles Taylor and Olivia Troye, two Trump administration officials who became vocal critics, also signed.

But a number of Republicans who did not sign a similar letter on behalf of Mr. Biden in 2020 signed the one for Ms. Harris this time, including several former House members, like Charles W. Boustany Jr. of Louisiana, Barbara Comstock of Virginia, Dan Miller of Florida and Bill Paxon of New York.

In their letter, the Republicans acknowledged concerns about “some of the positions advocated by the left wing of the Democratic Party,” and some of them have been quite critical of the Biden-Harris administration. Just last year, Mr. Zoellick wrote a newspaper essay eviscerating Democratic economic policies. But the letter said that “any potential concerns” about Ms. Harris “pale in comparison to” those over Mr. Trump.

To the extent that Mr. Trump was focused, it was on repeatedly vowing that his tariffs would revitalize the auto industry in Michigan, a crucial battleground state, and that a Trump loss in November would be catastrophic — referring to such an outcome as a “tragedy.”

Using the dire language he often uses to frame this election, he said if “we don’t win, there will be zero car jobs, manufacturing jobs.”

“It will all be out of here,” he said.

Speaking to thousands of supporters in the Dort Financial Arena in Flint, he also insisted vaguely that his tariff proposals would be enough to reverse a decades-long decline in the American auto industry and bring “so many auto plants” into the state if elected.

Mr. Trump’s propensity for lengthy answers that jump from topic to topic was often on display. Asked by a Ford employee about the threats to manufacturing jobs, Mr. Trump immediately responded by discussing the threat of nuclear war and climate change before talking about trade policy.

And while answering, he blamed China for the Covid pandemic and said he would meet next week with Prime Minister Narendra Modi of India, a country he called “a very big abuser” of American trade policy.

Mr. Trump briefly recounted the incident on Sunday at his golf course in West Palm Beach, Fla., commending the Secret Service on its response to the second apparent attempt on his life while also saying he needed “more people” on his protective detail.

After two days in which he and his campaign have, without evidence, blamed Democrats’ language both for the shooting he survived in Butler, Pa., and for the incident on Sunday, Mr. Trump suggested that foreign nations upset with his trade proposals might be to blame.

After discussing his plan to put a 200 percent tariff on cars imported from Mexico, Mr. Trump said: “And then you wonder why I get shot at, right? You know, only consequential presidents get shot at. When I say something like that, you have countries saying, ‘This guy.’ But what can you do?”

Mr. Trump to some extent softened his criticism of President Biden and Vice President Kamala Harris, thanking them for calling him after Sunday’s episode. Even as he described the conversations as “very nice,” the crowd erupted in a chorus of boos.

Over roughly an hour, Mr. Trump took just three questions from audience members and two from the town hall’s moderator, Gov. Sarah Huckabee Sanders of Arkansas, who more often made supportive statements that cleared the way for Mr. Trump to cycle through the same points that have animated his campaign.

Mr. Trump repeated his false insistence that he won in 2020, saying that “bad, bad things happened” that year, an allusion to his debunked claims of voter fraud. He insisted that he would curb inflation by raising U.S. oil and gas production, which has hit highs under the Biden administration.

As he was discussing energy policy, he at one point confused Bagram Air Base, which he makes central to his complaints about the Biden administration’s handling of the withdrawal from Afghanistan, with the Arctic National Wildlife Refuge in Alaska, which he opened up to oil and gas development during his presidency.

“We have Bagram in Alaska,” he said while talking about energy. “They say it might be as big, might be bigger than all of Saudi Arabia. I got it approved.”

Seconds later, he seemed to realize his mistake and tried to correct course. “Check that one out, Bagram. Check that one out. It’s, it’s — no, think about this: Between Bagram, between — you go to ANWR, you take a look at the kind of things that we’ve given up. We should be — we should have that air base, we should have that oil.”

Later, Mr. Trump claimed that his remarks, which at rallies and town halls often veer off course, were not rambling but had been intentional. After falsely asserting that people do not leave his rallies, a rebuttal of a jab Ms. Harris made at their debate, he said, “I give these long, sometimes very complex sentences and paragraphs, but they all come together.”

Mr. Trump’s event in Flint was his third town hall-style stop in three weeks. His campaign hosted one last month in Wisconsin that was moderated by Tulsi Gabbard, the former Democratic congresswoman who recently endorsed him, and then Mr. Trump took part in another hosted by Fox News’s Sean Hannity in Harrisburg, Pa.

Michigan is a critical battleground state that both campaigns are eyeing as they look for a path to victory in November. Mr. Trump’s running mate, Senator JD Vance of Ohio, held an event in Western Michigan earlier on Tuesday. Ms. Harris will also visit the state on Thursday, when she takes part in a livestream with Oprah Winfrey.

Mr. Trump won Michigan in 2016 by less than 0.3 percent, then lost it by about 2.8 percent four years later. Polls have shown Mr. Trump losing ground in the state since Ms. Harris became the Democratic nominee.

Simon J. Levien contributed reporting.

The firm had about 300 paid canvassers combined working on behalf of America PAC in those states, according to two of the people. But the PAC felt the group was not reaching enough voters quickly enough, the people said. The PAC has increased the number of doors it hopes to hit, according to the third person, reflecting the group’s belief that the switch will allow it to scale up and help Mr. Trump in the long run.

Arizona and Nevada are especially difficult for political canvassers working in the summer, given the daytime heat. The firm had knocked on about 250,000 doors in Arizona and about 150,000 doors in Nevada during its three-week engagement.

America PAC plans to try to rehire as many of the canvassers as possible, one of the people said, although it is unclear how many of them will stay under the new management. Some of the canvassers in Nevada, for instance, are already planning to work this week for a different candidate in the state, Sam Brown, the Republican candidate for Senate, said two of the people.

Still, there is precious little time before the election for these changes: Arizona begins early voting on Oct. 9, and Nevada voters can cast ballots as soon as Oct. 19. The super PAC has not been knocking on doors over the past few days in the two states, as the group tries to rebuild its field infrastructure there, two of the people said.

Both America PAC and the September Group declined to comment.

The move is significant because outside groups like Mr. Musk’s are shouldering an unusual amount of work for the Trump cause. The Trump campaign is taking advantage of recent federal election guidance that allows it to coordinate much more closely with super PACs, and America PAC has been central to that strategy. Every tactical shift is being closely watched by Republican insiders, especially those who are concerned about the risks in Mr. Trump’s voter turnout plan that depends on these outside groups.

This week’s change follows a larger shake-up at the super PAC this summer, when America PAC jettisoned In Field Strategies, which effectively ran the entire field campaign for the super PAC after receiving $21 million from the Musk group. After a lull of a few weeks, the super PAC hired new organizers and recently began spending big money again, disbursing $36 million on expenditures to help Republicans over the last month, according to federal filings.

Mr. Musk, the world’s wealthiest person, has been intimately involved in the super PAC’s operation, with plans to donate as much as $180 million to back the Trump effort. It is unclear what role he played in the decision in Arizona and Nevada, although his top aide visited the field operation in Nevada in recent days to get an up-close look at how it was faring, two of the people said.