Madeleine Albright, the first ever female Secretary of State, told supporters of Democratic presidential candidate Hillary Clinton that "there's a special place in hell" for women who don't help each other. (Reuters)

On the eve of the New Hampshire primary, Hillary Clinton’s quest to become the country’s first female president has encountered an unexpected problem: She is having trouble persuading women, young and old, to rally behind her cause.

The latest sign came Sunday, when a new CNN-WMUR survey here showed Sen. Bernie Sanders of Vermont beating Clinton among women by eight percentage points — which represents a big shift from the results last week in the Iowa caucuses, where Clinton won women by 11 points.

The survey followed unintentionally problematic comments over the weekend by Madeleine Albright and Gloria Steinem, older trailblazers who were trying to encourage younger women to support Clinton.

Steinem apologized Sunday for saying on a TV appearance Friday night that younger women were supporting Sanders because “the boys are with Bernie.” On Saturday, Albright drew criticism for saying that “there’s a special place in hell for women who don’t help each other,” even though she has expressed that sentiment many times before.

Clinton’s struggles with women underscore the extent to which she has not yet figured out how to harness the history-making potential of her candidacy in the same way that Barack Obama mobilized minorities and white liberals excited about electing the first black president.

Young women listen to Democratic presidential candidate Hillary Clinton as she speaks at Great Bay Community College in Portsmouth, N.H., on Feb. 6. (Jacquelyn Martin/AP)

Cognizant of the challenge, the Clinton campaign has sought in recent days here to address the problem, tweaking her speeches to put a focus on Clinton as an advocate for women. Clinton spent part of Friday with a group of female U.S. senators she calls the “sisterhood of the traveling pantsuits.”

At the Saturday event with Albright, Clinton offered an aspirational message — saying that the country’s history is “one of rising, of knocking down barriers, of moving toward a more perfect union” — that appeared designed to present her candidacy as a milepost on that national journey.

In an appearance on NBC’s “Meet the Press” on Sunday, Clinton defended Albright, saying that her words were a “lighthearted but very pointed remark, which people can take however they choose.”

“I think what she was trying to do, what she’s done in every setting I’ve ever seen her in going back 20-plus years, was to remind young women, particularly, that you know, this struggle, which many of us have been part of, is not over,” Clinton said.

Steinem wrote on her Facebook page that her remarks to comedian Bill Maher in which she seemed to say that pro-Sanders feminists were just looking for dating opportunities was a case of “talk-show Interruptus.”

“I misspoke on the Bill Maher show recently, and apologize for what’s been misinterpreted as implying young women aren’t serious in their politics,” she wrote.

Even so, Steinem’s comments pointed to the unexpected obstacle facing Clinton and her backers: a deep divide among women and feminist activists over how voters should respond to her.

While many older women’s rights advocates see the election of Clinton as the next logical step in a broader movement, some younger activists have expressed resentment at the notion that they should feel obligated to vote for Clinton simply because she’s a woman. Some have argued in recent months that Sanders, with his calls to end income inequality and make college free, is arguably the more feminist candidate.

“Hillary doesn’t seem to address those huge issues,” said Alexis Isabel Moncada, whose @feministculture Twitter account launched in April and boasts 170,000 followers.

Moncada, who is 17 but will be old enough to vote in November, said Clinton’s personal wealth and her life as a former first lady and secretary of state create a “disconnect with the entirety of women.”

On the trail, Clinton has begun to show more openness and reflection about the challenges of running as a woman in office, sometimes in response to challenges from other women.

At a student town hall at New England College on Saturday, a young woman told Clinton that she supported her in 2008 but has doubts about her candidacy now.

“My concern is that your answer that nothing new was found in the Benghazi hearings continues to give me some doubts,” the woman said. “Everybody knows you can’t write 30,000 emails to your yoga instructor.”

Another young woman asked why her peers think that Clinton is too buttoned up and “rehearsed.”

“I do have a somewhat narrower path that I’ve tried to walk. I do think sometimes it comes across as a little more restrained, a little more careful, and I’m sure that’s true,” Clinton answered. “It’s not just about me, it’s about young women, women of all ages, the expectations that are put upon you and how you deal with them and how you find your true voice and how you stand up for yourself and who you become.”

Many women’s rights advocates say they are proud to back Clinton, not just because of her gender but also because of her vast experience as a lawyer, first lady, senator and secretary of state.

In recent weeks, Clinton has won endorsements from numerous women’s rights organizations, including the Planned Parenthood Action Fund, the National Organization for Women, Emily’s List, NARAL Pro-Choice America and the Feminist Majority.

Feminist Majority’s president, Eleanor Smeal, who launched a campaign on Clinton’s behalf, She Wins We Win, said in an interview that Clinton has not only fought for women’s rights here and overseas but is “probably the strongest single candidate that has ever challenged for the presidency.”

Some have argued that they will vote for Clinton precisely because she’s a woman.

“There has never been a president who knows what it’s like to menstruate, be pregnant, or give birth,” Kate Harding, 41, wrote in the online women’s magazine Dame shortly after Clinton declared her candidacy. Nor, Harding said, has there been a president who has faced such blatant sexism “for showing too much cleavage, or having ‘cankles,’ or wearing unflattering headbands.”

A question for Clinton is whether she can use what is looking to be an extended primary campaign against Sanders to energize women for the general election should she win the nomination.

Republican front-runner Donald Trump traded accusations of sexism with Clinton, prompting a reexamination of the support Clinton won from feminists in the ’90s when she defended her husband against accusations that threatened to derail his presidency.

Kate Michelman, a former NARAL president and a prominent supporter of Clinton’s candidacy, echoes Clinton’s own evocation of a “vast right-wing conspiracy” in arguing that “the forces of sexism and anti-feminism are going to be loud and clear in their attempt to make sure no women get the presidency of this country.”

And some self-identified feminists say they feel less urgency to elect a woman in 2016 than they did eight years ago, perhaps because this is the second time a woman has come so close.

Shelby Knox, 29, subject of a documentary about campaigning for sex education in Texas schools, was living and working with Steinem in 2008 and said she found the attacks so painful she was “almost scared” to see Clinton announce again.

“When Hillary lost, I had this horrible fear that Gloria [Steinem] would never see a woman president,” said Knox, “as if the nation would reject any woman.”

This time around, she is confident Clinton will win. And even if she doesn’t, Knox thinks she will live to see a female president.

“It will be impossible for us not to have a woman president,” she said. “I have no doubt it will happen.”

Sellers reported from Washington. Karen Tumulty in Concord contributed to this report.