Interviews with voters found that Mr. 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, Pa. The recent string of attacks Mr. Trump has unleashed, particularly his criticism of the family of a Muslim soldier killed in Iraq, left Mr. Kinney disappointed. Faced with the choice of voting for Mr. Trump or Mrs. Clinton, Mr. Kinney said he may just stay home.  Two national polls conducted this month have Mrs. Clinton catching up to Mr. Trump among men over all. An NBC News/Wall Street Journal poll shows Mrs. Clinton with 43 percent support among men to his 42 percent. A Bloomberg Politics survey put Mr. Trump with a low-single-digit lead among men, according to the pollster who conducted the survey, Ann Selzer.  Get the latest national and state polls on the presidential election between Hillary Clinton and Donald J. Trump.  Mr. Romney relied on his 27-point edge among white men to carry the male vote over all, but Mr. Trump is even more reliant on them because of how poorly he performs with nonwhite voters. If Mr. Trump is only doing as well or worse than Mr. Romney did with white men, he will never make up the votes he is losing among women and nonwhites.  Mr. 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 Mr. Trump saw in the Republican primaries, he is most vulnerable with white men who have a college education or higher. Mr. Romney won that group, which votes at a higher rate than those without college degrees, by 21 points. Recent national polls have put Mr. 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 Mr. Trump losing over all to Mrs. Clinton. “And that is problematic for Trump given his need to appeal to whites.”  Mr. 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 last week by Fox News, had Mr. Trump with just 20 percent support, below the 27 percent that Mr. Romney received in 2012.  Even under the rosiest projections of white turnout, Mr. 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 Mr. Trump to win. He used the most recent ABC News/Washington Post poll of registered voters that had Mrs. Clinton beating Mr. Trump in a nationwide two-way race, 50 percent to 42 percent. It was among the better polls for Mr. Trump lately.  Mr. 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, Mr. Frey found, Mrs. Clinton would still win the popular vote by 1.1 million.  And Mr. 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, Mr. 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 Mr. 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,” Mr. Williams said in an interview. He plans to vote for Mrs. Clinton or Gary Johnson, the Libertarian Party candidate.  An especially worrisome problem for Mr. Trump lies in some of the white, heavily blue-collar states he hopes to put in play, like Ohio. Mr. Trump is nearly tied there with Mrs. 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 Mr. Trump’s deterioration with men puts him in an electoral hole, Mr. Romney won men in Ohio by seven percentage points four years ago. But that was still not enough. President Obama won the state, capturing 51 percent of the vote to Mr. Romney’s 48 percent.
It appears that after a stream of provocations, insults and reckless remarks, Mr. Trump has damaged himself with the one demographic that stands as a bulwark to a Clinton presidency.