After Sen. Marco Rubio of Florida insisted at the Republican presidential debate that rape and incest victims should carry pregnancies to term, aides to Hillary Rodham Clinton rushed to tell reporters at her headquarters that his unyielding stance would hurt Rubio with female voters.

When Donald Trump chose Friday to stand by his slights against women during the debate, saying Fox News journalist Megyn Kelly “behaved very badly” as a moderator — and then promoting a tweet calling her a “bimbo” — the chairwoman of the New Hampshire Republican Party accused Trump of chauvinism.

And in response to multiple male candidates saying they would shut down the federal government over financing for Planned Parenthood, the Democratic National Committee emailed talking points to allies within an hour saying that among the losers at the debate were “American women, who were attacked at every turn.”

Republican Party leaders, whose presidential nominees have not won a majority of female voters since 1988, are setting their sights on making electoral gains among women in the 2016 presidential race and trying to close the gender gap in swing states like Florida and Colorado. But the remarks and tone about women at Thursday’s debate — and the optics of 10 male candidates owning the stage — may have only damaged the party’s standing among female voters in the 2016 general election, according to pollsters and some Republican leaders.

“So much of the debate was all about appealing to male voters and other parts of the Republican debates, rather than doing anything to help the party’s general election goal of trying to be more inclusive,” said Lee M. Miringoff, director of the Marist College Institute for Public Opinion. “By being callous or showing disregard toward women, and then laughing it off with a charge of political correctness or simply saying they’re taking conservative stands, the Republicans could win over some of the older male Republican voters out there. But what about female voters?”

Democrats were gleeful at the tone of the debate, already imagining future campaign advertisements featuring debate cutaways featuring Rubio saying that future Americans will “call us barbarians for murdering millions of babies.”

In the short term, however, the political peril for the Republican candidates may not be so grave. They are largely focused now on winning over likely Republican voters who will decided the party’s nomination — an electorate that tends to skew male and older in many key states.

Recent polls of Republican voters indicate Trump is performing strongly among men and to a slightly lesser extent among women, though sizable numbers of women also say they would not support him. It remains an open question whether Trump offended his supporters, or many other likely primary voters, by refusing to renounce his past descriptions of women as “fat pigs” during the debate; indeed, pollsters say he may have struck a chord with some voters by saying he doesn’t “have time for political correctness” when he was asked about his remarks.

With the possibility that a woman could be the nominee of a major political party for the first time, Republicans are facing the likelihood of an even more complicated environment than they have had in recent presidential elections. Gallup polls show that female voters have been favoring the Democratic presidential nominees since the 1990s, often by increasingly large numbers.

The 2012 election was a case in point: Even though Mitt Romney, the Republican nominee, won white women with 56 percent of their votes, he lost overall with female voters. A Republican nominee would be hard-pressed to improve that if the 2016 Democratic nominee is a woman, many Republican pollsters believe.

Several prominent Republican women said they were worried that the candidates would only hurt themselves, and the party, if they did not change the substance and style of their remarks at future debates, which will held monthly this fall and winter. Thursday’s debate attracted an enormous audience of 24 million viewers; the next debate will be Sept. 16 and broadcast on CNN.

“Not one candidate attempted to persuade women voters,” said Margaret Hoover, a Republican consultant and author. “The GOP needs to fight for women votes because it believes our policies are better for women. There’s a difference between pandering and vote-courting: Thursday night, GOP candidates did neither for women weary of the Republican brand.”

On abortion, Rubio, former Florida Gov. Jeb Bush and Wisconsin Gov. Scott Walker all gave no ground, unlike the remarks by some Republicans on other social issues like same-sex marriage.

Walker’s stated opposition to an abortion ban exception to protect the life of the mother, for instance, prompted a tweet from the Clinton campaign — “Problem for Scott Walker: 24 million people heard how out of touch he is on women’s health” — but also teeth-gnashing from some female Republicans.

“For Walker, the question of not sparing a mother’s life if endangered by a pregnancy seeds an extremist view that would be quite unpopular in a general election,” Hoover said.

Jennifer Horn, the Republican chairwoman in New Hampshire, focused her frustrations on Trump, who leads recent opinion polls for that state’s first-in-the-nation primary.

“Megyn Kelly is an intelligent, successful, educated, professional woman, and the comments and tweets from Donald Trump were demeaning and chauvinistic,” Horn said. “There’s a big difference between being politically correct and being respectful, and Thursday night Donald Trump was not respectful to women.”

Whit Ayers, a veteran Republican pollster who is advising Rubio’s campaign, said that “Trump only hurts Republicans among women if he becomes the nominee, which he won’t.”

He added, “The Republican image and the Republican brand will be defined by the Republican nominees for president and vice president, not what a losing candidate said in a debate 15 months before the election.”

Carly Fiorina, the only female Republican candidate in the presidential race, who was relegated to an earlier debate Thursday because of her low poll numbers, was circumspect about whether she would have challenged Trump had she been onstage with him. When asked if she would have denounced his comments, she insisted that she had, but then proceeded to do so only in generic, gender-agnostic terms about civility in politics.

“It’s not helpful to call people names, it’s not helpful to paint with a broad bush, it’s not helpful to engage in personal insult,” Fiorina said. “Some Republicans do that. Some Democrats do that. And I’ve called both of them out.”

Many Republicans had worried that Fiorina’s exclusion from the prime-time debate would expose the party to criticism that it was giving second-class treatment to its only female candidate. While onstage, she nonetheless had to endure some awkward moments with her male colleagues. When Rick Perry was answering a question about Iran, he said that he would prefer to have “Carly Fiorina over there doing our negotiation than John Kerry,” apparently an insinuation that she would be subordinate to a president.

It was not the first time Fiorina has been the subject of that kind of backhanded compliment. When asked what woman should be on the $10 bill at a candidates’ forum on Monday, Rick Santorum answered, “Carly is a pretty good choice.”

As for Trump, as he made the rounds to the morning talk shows, he seemed to show some signs of, if not quite contrition, at least regret that people could be left with the impression that he said something offensive to women.

“I don’t recognize those words,” he said on the MSNBC program “Morning Joe.” “Not that I’m an angel, by the way. But I don’t recognize those words.”

Any regret was fleeting. He also insisted that his “fat pigs” disparagement of Rosie O’Donnell during the debate was “the biggest event in terms of sound, and in terms of combustion in the room. It was the biggest event of the evening.”

© 2015 The New York Times Company