MANCHESTER, N.H. — She survived that early DNA debacle, withstood endless insults from the president, outlasted a bevy of other candidates. One thing Senator Elizabeth Warren hasn’t overcome is voter fears that a woman can’t beat Donald Trump.

The Massachusetts Democrat confronted those concerns head on during a CNN town hall event Wednesday night, when a woman in the audience asked Warren if she believes that her male rivals stand a better chance of beating the president based on gender alone.

“I believe they think so, but they would be wrong,’’ Warren replied.

As Warren seeks a strong showing in the state’s first-in-the-nation primary to help ensure her political survival, New Hampshire presents an opportunity for the leading woman in the primary race to excel. The state does, after all, have a strong track record of electing female Democrats to high office — the majority of its delegation in Washington is female, including both senators, who also both served as governor.

But some voters can’t shake the fear that it’s risky — maybe too risky — to nominate a woman to take on Trump.

“Some women, myself included, were very defeated by the Hillary Clinton defeat,’’ said Sylvia Larsen, a former president of the New Hampshire Senate. “And that somewhat dampens the enthusiasm to try it again right away."

While all the major candidates are facing questions about their electability, it’s clear the Warren campaign believes it also needs to wrestle with a unique question around gender. The senator leaned into those themes on the stump in Iowa, following her pointed remarks on the debate stage there that only she and Senator Amy Klobuchar — in contrast to the men standing next to them — had never lost an election.

Warren routinely highlights her defeat of a popular Republican male incumbent, Scott Brown, to win her Senate seat in 2012 as she makes a case for her own electability.

The broader electoral potency of women is a regular talking point for her on the stump now.

Asked at the town hall about whether her male rivals are better suited to take on Trump, Warren weaved her substantive answer with humor — a tactic experts on gender dynamics in politics say can help women candidates successfully tackle what can be a dangerous subject for them.

She pointed to 1960, when many Americans said the country wouldn’t elect a Catholic president, but John. F. Kennedy prevailed. “In 2008, a lot of folks said we can’t have an African-American nominee because we’ve never had an African-American president before. But our party is better than that, and we proved that our country is better than that. 2020 — we can and should have a woman for president."

Warren’s campaign then tweeted out a clip of the answer. “Since Donald Trump was elected, women have been outperforming men in competitive elections,’’ the tweet said. “It’s simple: Women win!’’

Some Warren supporters acknowledge it’s a question voters are grappling with.

“People do worry, but it’s an absurd worry because it’s a self-fulfilling prophecy,’’ said New Hampshire state Representative Joyce Weston, who is backing Warren.

Lisa DeMio, 53, a Warren supporter who owns a small business in Hampstead, said she is attracted to Warren’s candidacy because of their similar backgrounds. She likes Warren’s moral clarity and focus on solving income inequality.

But she also likes that Warren is a woman.

“I would be absolutely lying if I said it did not play into it," DeMio said.

But she said she also knows that some women and men think being a woman hurts Warren’s chances of winning in November. “It’s straight-up misogyny, but it’s also fear. People are terrified’’ of not beating Trump, “and rightfully so,’’ DeMio said.

Others echoed that sentiment.

“Unfortunately I still think we live in a patriarchal society,’’ said Lisa Morris, 53, a middle school teacher who came to listen to Warren speak at a theater in Salem on Thursday night. “I think people believe that a woman wouldn’t be able to stand up to the bullying of our current leader, and I don’t think that has any basis at all. I think she can completely handle herself.’’

Morris said that she is supporting Warren because of her substantive policy plans, but that her gender is a plus for her: “I love the fact that she’s a woman.’’

Like other female politicians, Warren is having to run “dual campaigns,’’ said Kelly Dittmar, assistant professor of political science at Rutgers University Camden and a scholar at the Center for American Women and Politics.

Warren has clearly had to spend time her male rivals haven’t explaining that she can win as a woman, “to put down doubts,’’ said Dittmar. “Certainly the audience for those sorts of answers and that conversation that she’s currently having is both men and women.’’

With five days to go before New Hampshire votes, Warren was making a pitch Thursday at a child care center in Exeter.

She met with about a dozen parents, teachers, and administrators to discuss her plan to provide affordable child care and pay early-childhood teachers more.

Not every New Hampshire Democrat sees gender complicating Warren’s path here. Several Warren supporters said they don’t hear concerns about a woman beating Trump much, if at all.

Kathy Sullivan, one of the state’s Democratic National Committee members who has endorsed Warren, said almost all of her friends are trying to decide between Warren and Klobuchar.

“We’re so used to electing women here that it’s really not an issue in New Hampshire as far as people being willing to vote for a woman,’’ said Sullivan, one of several voters to note how the state has elected women to nearly every top elected office, including sending an all-female delegation to Washington in 2012.

“The question right now is not gender,’’ when it comes to taking on Trump, said Arnie Arnesen, a Democratic activist and talk radio host from Concord.

“It’s not, ‘Can a woman defeat him?’ It’s, ‘Who the hell can defeat him?’ ’’

Liz Goodwin of the Globe staff contributed to this report.