But what is striking is the change in attitudes about Mrs. Clinton among those voters, and her struggle to win them over again. In dozens of interviews in diners, offices and neighborhoods across the country, many white male Democrats expressed an array of misgivings, with some former supporters turning away from her now.

Many said they did not trust her to overhaul the economy because of her wealth and her ties to Wall Street. Some said her use of private email as secretary of state indicated she had something to hide. A few said they did not think a woman should be commander in chief. But most said they simply did not think Mrs. Clinton cared about people like them.

“She’s talking to minorities now, not really to white people, and that’s a mistake,” said Dennis Bertko, 66, a construction project manager in Youngstown, Ohio, as he sipped a draft beer at the Golden Dawn Restaurant in a downtrodden part of town. “She could have a broader message. We would have listened.”

“Instead, she’s talking a lot about continuing Obama’s policies,” he said. “I just don’t necessarily agree with all of the liberal ideas of Obama.”

Mr. Bertko said that he rarely crossed party lines but that he voted for Donald J. Trump, who is making a strong pitch to disaffected white men by assailing free-trade agreements that Mrs. Clinton once supported. “I know a lot of guys who are open to Trump,” he said.

The fading of white men as a Democratic bloc is hardly new: The last nominee to carry them was Lyndon Johnson in 1964, and many blue-collar “Reagan Democrats” now steadily vote Republican. But Democrats have won about 35 to 40 percent of white men in nearly every presidential election since 1988. And some Democratic leaders say the party needs white male voters to win the presidency, raise large sums of money and, like it or not, maintain credibility as a broad-based national coalition.

To win a general election, Mrs. Clinton would rely most heavily on strong turnout from blacks, Hispanics, women and older voters. Though she won among white men in Arkansas, Alabama and Tennessee, and tied in Texas, some Democratic officials and pollsters say they fear that without a stronger strategy, Mrs. Clinton could perform as poorly among white men as Walter Mondale, who drew just 32 percent in 1984, or even George McGovern, who took 31 percent in 1972.

“Her most serious relationship problem is with white men, on a policy issue front but also stylistically, and she is at real risk for running worse than the average Democrat with white males,” said Peter Hart, a veteran Democratic pollster.

Bill Richardson, former governor of New Mexico and energy secretary under President Clinton, said Mrs. Clinton needed to focus more on economic issues and job creation and to deploy her husband on her behalf. “Priority needs to be given to stopping the erosion of the white male voter and Reagan Democrats to Republicans,” he said.

Mrs. Clinton’s advisers expressed confidence, saying her economic policies and national security experience would appeal strongly to white men in a general election. They said she regularly won among those over 45 and argued that Senator Bernie Sanders’s appeal among younger white men reflected his popularity with young people generally.

Joel Benenson, Mrs. Clinton’s strategist and pollster, predicted she would win at least 35 percent of white men nationally — the share Mr. Obama took in 2012 — and even more in battleground states like Ohio and Pennsylvania. But he insisted that focusing on white men overlooked the breadth of her support.

“Winning is never about slicing and dicing the electorate,” he said. “What you have to do is create a diverse coalition of voters that enables you to win, and win repeatedly. That’s what Hillary Clinton has done, and that’s what Bernie Sanders has failed to do.”

But Mrs. Clinton is clearly focusing more so far on nonwhites, who provide outsize shares of the delegates needed to win the nomination. Her political message, events and surrogate speakers have been geared largely to blacks and Hispanics, from denouncing gun violence and police abuses to promising improvements in immigration and education.

Eight years ago, Mrs. Clinton appealed to whites to counter Mr. Obama’s popularity among minority voters. She ran as a moderate and a national security hawk, and fondly recalled how her father taught her to shoot. Some political analysts said she also benefited among white men because many were not comfortable voting for a black man.

Mrs. Clinton’s political challenges now center on the controversies stemming from her time as secretary of state and doubts about her willingness to take on Wall Street.

“There are all these questions about her past, and she doesn’t give straight responses about them,” said Forrest Giffin, 23, a Democrat in Sumter, S.C., who cited Mrs. Clinton’s refusal to release transcripts of her paid speeches to banks. Mr. Giffin, a mall supervisor and assistant manager at a gas station, added, “I really wonder if she wants people like me in the Democratic Party.”

Terry Downs, a retired art professor who was impressed by Mrs. Clinton in Plymouth, N.H., last fall, said he was won over by Mr. Sanders’s economic policies. “I just thought there’s a lot of hypocritical lip service coming from Hillary when she talks like a strong progressive,” he said. “She and her husband received millions of dollars from Wall Street.”

In Ohio, a plurality of white men said honesty and trustworthiness were the most important qualities in a candidate, and 89 percent of them voted for Mr. Sanders, according to exit polls. Of the four in 10 who wanted a president to pursue more liberal policies than Mr. Obama’s, a wide majority favored Mr. Sanders.

In Youngstown, a city battered by job losses, Mrs. Clinton’s record was a flash point at the Golden Dawn.

“Being an ex-serviceman, the situation with Benghazi still upsets me greatly,” said Hayden Gerdes, 72, referring to the terrorist attacks in Libya. A Clinton voter in 2008, he chose Gov. John Kasich, a Republican, on Tuesday.

Mr. Gerdes had a sparring partner in Dick Lucarell, 73, who voted for Mrs. Clinton in 2008 and again on Tuesday. Mr. Lucarell said that Mrs. Clinton was the target of unfair Republican attacks, and that she and her husband would be “a strong team.” But he also said she had yet to give white men compelling reasons to stay in the party.

“If I’m a woman, I probably vote for Hillary. If I’m Hispanic, I vote for Hillary. Blacks will vote for Hillary,” Mr. Lucarell said. “But white people, especially white men — she has a big problem there.”