The year of the woman and the midterm gains that followed electrified Democrats, who have eagerly promoted themselves as the party of diversity. That success has inspired some of the most powerful women in politics to consider running for president. And it has boosted expectations that the political calculus for women has changed in the last two years, and that gender could become an asset, even in a presidential contest. Mrs. Clinton, after all, won the popular vote by almost three million.

Yet at a time of ascendancy for women in the party, there’s a lingering doubt in some quarters about whether there is a risk involved in nominating a woman to take on President Trump, whom Democrats fervently want to unseat.

The specter of Mrs. Clinton’s defeat in 2016 still haunts some Democratic officials, voters and activists. There is widespread recognition that women in politics are held to a different standard than men on qualities like likability and toughness, and that voters have traditionally been more reluctant to elect women as executives than as legislators.

Some women see bias in the excitement surrounding a potential presidential run by Beto O’Rourke, the Texan who energized the left in a losing Senate bid, while Stacey Abrams is not mentioned as a possibility even though she had a much narrower loss for governor of Georgia.

“There’s a real tension,” said Neera Tanden, the president of the Center for American Progress and a former policy adviser to Mrs. Clinton. “On one hand, women are leading the resistance and deserve representation. But on the other side, there’s a fear that if misogyny beat Clinton, it can beat other women.”