WASHINGTON — A day before his visit in May to Michigan, where unemployment has climbed to 23 percent and flooding had grown severe enough to make national headlines, President Trump threatened to “hold up funding” for a state he almost certainly must carry to win re-election.

The rationale behind this extraordinary warning and apparent act of self-sabotage? Two years after Michigan residents overwhelmingly approved no-excuse absentee voting, the secretary of state, Jocelyn Benson, a Democrat, said she would send absentee ballot applications to all voters.

Mr. Trump, signaling a willingness to wield the power of the federal government on behalf of his political interest, claimed such a distribution of applications was a “rogue” and “illegal” act that would lead to mass voter fraud.

Even before the coronavirus infected more than 56,000 residents and left it with the second-worst unemployment rate in the country, Michigan was shaping up to be the most difficult state for Mr. Trump to win a second time. Now his prospects there appear dimmer — in part because of his own conduct.

Michigan amounts to a one-state case study on how Mr. Trump’s impulsiveness, inattention to detail and penchant for personal insults have eroded his political standing and diminished his chances to win re-election.

In addition to his ultimatum over federal funding, Mr. Trump has ridiculed a half-dozen of the state’s female leaders, proposed cutting support for the Great Lakes and suggested a beloved former lawmaker from Michigan is in hell.

Even as the state moved aggressively to contain the coronavirus outbreak, Mr. Trump encouraged the types of protests that broke out in Michigan against the economic lockdown. And on Friday, the Trump administration weighed in against Gov. Gretchen Whitmer, a Democrat who is among those being vetted as a potential running mate for Joseph R. Biden Jr., in a lawsuit brought by some Michigan businesses over the lockdown imposed by the governor to deal with the coronavirus pandemic.

The Justice Department said it would support the suit, calling some of the constraints that Ms. Whitmer had imposed on the economy “arbitrary and irrational,” even though most of the restrictions have already been lifted.

“He’s singularly focused on energizing his base,” said former Representative David Trott, a Republican from suburban Detroit who did not seek re-election two years ago in part because of discomfort with Mr. Trump. “It worked in 2016 for him, but if I was advising him I’d say, ‘Look, you had the perfect storm in 2016.’”

But the president’s assault on Democrats in the state also illuminates how his threats to use the powers of his office on his campaign’s behalf often amount to little more than bluster, a bullying tactic that is not without short-term effect but in the end only unites and energizes his opponents.

In Michigan’s case, the state continues to receive its share of stimulus money and supplies needed to combat the virus, and the president’s scorched-earth tactics have brought him no apparent political benefit.

Every public poll in Michigan indicates the president is trailing in the state, and some Democrats believe it ultimately may not be very close there.

“You don’t win Oakland County by aligning yourself with men toting guns at the State Capitol and threatening to withhold federal funding in the time of a pandemic,” said Lon Johnson, a former state Democratic chair, alluding to the affluent suburbs outside Detroit.

Part of the president’s difficulties in the state are structural: Michigan is a Democratic-leaning state in federal elections, it has more black and college-educated voters than some other Midwestern battlegrounds and its manufacturing-heavy economy has been especially hard-hit by a virus that spreads in confined work areas.

To be sure, he still retains an intense following, in Michigan and in every competitive state, and profound questions remain about how Mr. Biden, the presumptive Democratic nominee, will stand up to the president’s anything-to-win tactics. Mr. Trump’s encouragement of demonstrators demanding faster action in reopening the economy in May helped spur on protesters in Michigan, some armed, leading at one point to the closing of the Capitol.

Mr. Trump’s advisers have nudged him to focus on his success in pushing through the renegotiated trade pact with Mexico and Canada, which has benefits for the auto industry and, were he to make it more of an issue, could help him with working-class voters in Michigan.

And they are hoping that the presence on the ballot in Michigan this year of John James, an African-American Republican who is running for a U.S. Senate seat, could peel away some black voters from Democrats. Indeed, Mr. Trump’s decision to include Mr. James at an ostensibly nonpolitical round table with black Michiganders at a Ford plant in May angered prominent state Democrats, according to Democratic officials.

Michigan, however, offers a vivid illustration of how Mr. Trump can be his own worst political enemy.

He delights in headline-grabbing and often menacing attacks but rarely follows through with the punishment he threatens, leaving him looking more like a peanut gallery heckler than a political force to be feared.

That was true in the case of the clash in May. Hours after threatening to defund Michigan, Mr. Trump told reporters, “I don’t think it’s going to be necessary” and, speaking to the news media in the state the next day, said he was “not going to discuss” what funds he had in mind.

Similarly, after insulting Ms. Whitmer as “half Whitmer” and “the woman in Michigan” while suggesting to Vice President Mike Pence that he ignore her calls entirely, Mr. Trump himself quietly telephoned her to ensure that a shipment of personal protective equipment had arrived in the state.

This pattern of attack-and-retreat instills little fear in his adversaries, reinforces negative perceptions about him among voters (who often only hear of the threats) and hands Democrats fodder for their own reprisals.

In an interview, Ms. Whitmer sought to turn Mr. Trump’s attacks to Democratic advantage, suggesting that the citizens of her state could be hurt because of Mr. Trump’s contempt for her.

“Certainly, the concern that the people of Michigan might be punished because someone isn’t a fan of mine is an unfortunate concern that we have to have right now,” Ms. Whitmer said.

Influential Michigan Republicans are growing alarmed by the president’s prospects and have taken steps to steer him away from what they acknowledge is his self-defeating conduct.

Lee Chatfield, the speaker of the State House, said he would like to see a better partnership between the state and federal government in dealing with the coronavirus crisis.

“I want both the governor and the president to be successful and I’ve made that very clear to him,” Mr. Chatfield said. “The closer we partner together and communicate, the more successful Michigan will be.”

Representative Fred Upton, the longest-serving member of Michigan’s congressional delegation, has also sought to defuse tensions between Mr. Trump and Ms. Whitmer. “We don’t need finger jabbing because it’s only going to hurt people across the state,” Mr. Upton said.

He and other Michigan Republicans have repeatedly urged the White House to focus on slowing the virus and rebuilding the economy but have been dismayed by his repeated return to taunts, insults and conspiracy theories.

Mr. Upton said that after Mr. Trump continued to accuse the MSNBC anchor Joe Scarborough of killing a woman who worked for him when he was a Republican member of Congress, he sent a text message to Mark Meadows, the White House chief of staff.

“I said, ‘Maybe it sells in North Carolina, it doesn’t win Michigan,’” Mr. Upton recalled.

Mr. Trump’s advisers recognize the importance of the state. That’s why they set up an event during his visit in May aimed at two Democratic-leaning constituencies, union workers and African-Americans.

Among those at the Ford plant round-table with black community leaders was Karen Whitsett, a Democratic state lawmaker who contracted the coronavirus but has been shunned by her own party for appearing with Mr. Trump in April at the White House and echoing his endorsement of the antimalarial drug hydroxychloroquine.

Ms. Whitsett said Mr. Trump had telephoned her after her visit to ask how she was doing, and how he could help her district, while his son-in-law, Jared Kushner, did the same after the meeting in Michigan.

By contrast, she said she had never heard from Mr. Biden despite having endorsed his candidacy, and she is now uncertain whom she will vote for.

Yet Mr. Trump has regularly undermined his broader outreach efforts.

His attacks on former President Barack Obama, who won two decisive victories in the state, demeaning descriptions of women and immigrant communities and playing down of the coronavirus, which has disproportionately affected both African-Americans and older adults, “describes about 70 percent of Michigan’s population,” said Representative Dan Kildee, a Democrat from Flint.

Mr. Trump seems to have almost gone out of his way to target high-profile Michigan women. In addition to his attacks on Ms. Whitmer and Ms. Benson, he has targeted the chief executive of General Motors, Mary T. Barra (“a mess”), Attorney General Dana Nessel (“wacky”), Representative Rashida Tlaib (who is of Palestinian descent and is part of “the squad,” who Mr. Trump said should “go back” to their native countries) and Representative Debbie Dingell.

Mr. Trump has repeatedly sought to humiliate Ms. Dingell by insisting she did not fully appreciate his efforts to honor her husband, former Representative John D. Dingell, who died last year. And shortly before Christmas last year, at a rally in Michigan, the president mocked Ms. Dingell at length and suggested that Mr. Dingell might be “looking up.”

His comments prompted bipartisan condemnation, including from Mr. Upton, who said he told the president he needed the sort of union autoworkers who formed the core of Mr. Dingell’s coalition.

Ms. Dingell said Mr. Trump never apologized to her.

Largely detached from the details of policymaking, he inflicted a wound on himself by proposing budgets that nearly eliminate federal spending on Great Lakes restoration, a bipartisan priority in the state. Mr. Trump reversed course once the state’s congressional delegation buttonholed him on the issue, but Democrats still have ready-made material on an issue dear to the heart of many Michiganders.

A number of Michigan Republicans believe the president can still carry the state. Their faith stems in part from how he defied the odds, and some late polls, four years ago to become the first Republican to win Michigan in nearly three decades, even if it was by the smallest of margins: 10,704 votes out of 4.8 million votes cast.

“He was underestimated in 2016 and he’s being underestimated now,” said John Truscott, a longtime Michigan Republican strategist. “The heavy pall of Covid over everything right now will be much different by the fall and how the country comes out of this will be a big determining factor.”

How Mr. Trump is perceived to have led the country in the crisis, however, will be central. And if he does not change his divisive behavior, voters may render their own verdict as much on him as on the impact of the virus.

“There is a tremendous hunger for honest differences of opinion that don’t devolve into personal attacks,” said Rich Studley, the chief of the Republican-leaning Michigan Chamber of Commerce. “We need bold and sincere, thoughtful and caring leadership. I don’t think only negative messages will play very well at all.”

Jonathan Martin reported from Washington, and Kathleen Gray from Lansing, Mich., and Detroit. Maggie Haberman contributed reporting from New York.