Donald Trump’s support among white men, the linchpin of his presidential campaign, is showing surprising signs of weakness that could foreclose his only remaining path to victory in November.

If not reversed, the trend could materialize into one of the most unanticipated developments of the 2016 presidential campaign: That Hillary Clinton, the first woman at the head a major party ticket and a divisive figure unpopular with many men, ends up narrowing the gender gap that has been a constant of American presidential elections for decades.

Surveys of voters nationwide and in battleground states conducted over the past two weeks showed Trump was even with or below where Mitt Romney, the Republican Party nominee four years ago, was with white men when he won that demographic by an overwhelming 27 percentage points.

For Trump, who has staked much of his legitimacy as a candidate on his strength in the polls, the numbers are a dose of cold, dangerous math. If he does not perform any better than Romney did with white men, he will almost certainly be unable to rally the millions of disaffected white voters he says will propel him to the White House.

All along, one of the central questions of the election has been whether there are enough white men who will turn out to vote to lift Trump to victory. And there may be enough, demographers and pollsters said.

But for now it appears that after a ceaseless stream of provocations, insults and reckless remarks, Trump has damaged himself significantly with the one demographic that stands as a bulwark to a Clinton presidency.

“If you set out to design a strategy to produce the lowest popular vote possible in the new American electorate of 2016, you would be hard-pressed to do a better job than Donald Trump has,” said Whit Ayres, a pollster who has advised Republican presidential and Senate candidates for more than 25 years. “This is an electoral disaster waiting to happen.”

There are still nearly three months before Election Day, ample time to shift the dynamics of the race. But the question Republicans inside and outside the Trump campaign are asking is whether the damage Trump has caused himself during the last few weeks is irreparable.

Interviews with voters found that Trump’s increasingly outlandish behavior was rubbing many in his key voting bloc the wrong way.

“I liked Trump until he opened his mouth,” said Phil Kinney, a retired middle school administrator and a Republican from Bethlehem, Penn. The recent string of attacks Trump has unleashed, particularly his criticism of the family of a Muslim soldier killed in Iraq, left Kinney disappointed. Faced with the choice of voting for Trump or Clinton, Kinney said he may just stay home.

Two national polls conducted this month have Clinton catching up to Trump among men overall. An NBC News/Wall Street Journal poll shows Clinton with 43 percent support among men to his 42 percent. A Bloomberg Politics survey put Trump with a low-single-digit lead among men, according to the pollster who conducted the survey, Ann Selzer.

Romney relied on his 27-point edge among white men to carry the male vote overall, but Trump is even more reliant on them because of how poorly he performs with nonwhite voters. If Trump is only doing as well or worse than Romney did with white men, he will never make up the votes he is losing among women and nonwhites.

Trump’s troubles with white men do not end there. The data reveal a huge gap in those who have a college education and those who do not. As Trump saw in the Republican primaries, he is most vulnerable with white men who have a college education or higher. Romney won that group, which votes at a higher rate than those without college degrees, by 21 points. Recent national polls have put Trump’s support with them far lower.

“We’re looking at a margin among college-educated white men for him that’s less than half what Romney won,” said Gary Langer, an independent pollster who conducted an ABC News/Washington Post survey this month that showed Trump losing overall to Clinton. “And that is problematic for Trump given his need to appeal to whites.”

Trump’s difficulties with men are symptoms of a larger vulnerability: disapproval that runs deeply through many segments and subgroups of the voting population.

Self-identified Republicans, white women, the wealthy and well-educated people of all races are turning their backs on him. Two national polls have recently put his support from African-Americans at an astonishing 1 percent. Separate Wall Street Journal/NBC News/Marist surveys in Ohio and Pennsylvania from July found that zero percent of black voters said they planned to vote for him. The latest poll of Latinos, conducted within the past week by Fox News, had Trump with 20 percent support, below the 27 percent that Romney received in 2012.

Even under the rosiest projections of white turnout, Trump would still lose the popular vote if his poll numbers among whites do not improve considerably.

William H. Frey, a demographics expert with the Brookings Institution, a nonpartisan think tank, conducted several simulations that tried to determine how much the turnout among white men without college educations would have to increase for Trump to win. He used the most recent ABC News/Washington Post poll of registered voters that had Clinton beating Trump in a nationwide two-way race, 50 to 42 percent. It was among the better polls for Trump lately.

Frey tested different turnout assumptions, including improbably optimistic ones, like if 99 percent of white, non-college-educated men turned out to vote. None of the chain of events produced a Trump victory.

In fact, even if virtually all of the white, non-college-educated men eligible to vote did so, Frey found, Clinton would still win the popular vote by 1.1 million.

And Frey said he did not account for the expected growth in Hispanic turnout. “Once you build that in,” he said, “it’s even worse for Trump.”

By not appealing more broadly to African-Americans, Hispanics and other minority groups, Trump is precariously reliant on a segment of the population that is a shrinking portion of the electorate.

White voters were 88 percent of the electorate in the 1980 election, a figure that has declined a few percentage points every four years since then. By 2012, the white vote was down to 72 percent. Most estimates for 2016 put it at or below 70 percent.

And if Trump keeps alienating more of them like Gary Williams, a lifelong Republican and small-business owner from Lexington, Tenn., his base will continue to shrink. “He cusses in front of women and children and everybody else. He’s not a Christian. Everything about him makes me sick,” Williams said in an interview. He plans to vote for Clinton or Gary Johnson, the Libertarian Party candidate.

An especially worrisome problem for Trump lies in some of the white, heavily blue-collar states he hopes to put in play, like Ohio. Trump is nearly tied there with Clinton among men, with 42 percent to her 41 percent, according to an NBC News/Wall Street Journal/Marist poll conducted the first week of August.

Illustrating just how much Trump’s deterioration with men puts him in an electoral hole, Romney won men in Ohio by 7 percentage points four years ago. But that was still not enough. President Barack Obama won the state, capturing 51 percent of the vote to Romney’s 48 percent.

© 2016 The New York Times Company