Some white men have proved to be within reach: single men, college students and graduates with advanced degrees, the nonreligious, and gay men. But working-class married men remain hardest to win over and, unless they are in unions, get the least attention — to the dismay of some partisans.

“You can’t just give Republicans a clear field to play for the votes of white working-class men without putting up some sort of a fight because that just allows them to run the table with these voters, thereby potentially offsetting your burgeoning advantage among minorities, single women, millennials,” said Ruy Teixeira, an analyst at the left-leaning Center for American Progress.

“I just think Democrats are having a hard time figuring out how to effectively pursue it,” he added.

What discourages Democrats is that men’s attitudes shaped over generations — through debates over civil rights, anti-Communism, Vietnam, feminism, gun control and dislocations from lost manufacturing jobs and stagnant wages in a global economy — are not easily altered.