And Senator Amy Klobuchar of Minnesota talks openly about the double-bind of being a woman in politics. “You also have to show you can do tough jobs and then people say you’re too tough. Like you can’t win, right? But you, again, have to just deal with that,” she said, in a May interview with Pod Save America.

Ms. Gillibrand distinguished herself by running on what she called a “women plus” campaign platform. She announced her candidacy with a focus on her family, saying that as a mother of young children she would fight just as hard for other people’s kids, too. Her campaign logo was Barbie pink, and her slogan — “brave wins” — a reference to a children’s book she wrote profiling famous suffragists.

In May, Ms. Gillibrand went to Atlanta for an event on abortion rights, telling a reporter that she was going “to lead the fight against these unbelievable, draconian inhumane abortion bans.” During the Democratic primary debates, she proactively brought up topics relating to issues like gender dynamics and reproductive rights, more than nearly all the other candidates, according to an analysis by the Women and Politics Institute at American University and the Barbara Lee Family Foundation , which studies and supports women in politics.

Those moments and others like them, when she leaned the most into her feminist credentials, were the times when her campaign got the most traction, say strategists and those who study women and political power.

“The question is, how do you break through in this environment?” said the Democratic operative Christina Reynolds, vice president of communications at Emily’s List. “What Kirsten Gillibrand showed is speaking directly to women’s issues and women’s voters might get you a little breakthrough.”

Tresa Undem, a pollster who specializes in surveys on gender issues, said that discussions of fairness and power carry more political currency than they used to just a few years ago. Voters have started using terms like misogyny and patriarchy in focus groups — words Ms. Undem never heard mentioned until Donald Trump won the White House.