At town halls and political events in New Hampshire, where she has made far more campaign stops than her rivals, Nikki Haley has mostly sidestepped any discussion of abortion, a fraught issue for the Republican Party.

As the G.O.P. activist base tries to pull state lawmakers further to the right in curbing access to abortion, moderates worry that the hard-line stance has already handed electoral wins to Democrats and could have dire consequences in 2024. Ms. Haley, a former governor of South Carolina and United Nations ambassador, has tried to pull off a difficult balancing act on the issue, and her attempts haven’t always resonated — partly because, her critics say, she has avoided discussing details.

On Tuesday, with more than 100 people gathered in a drizzle for a town hall at a picturesque vineyard in Hollis, Christina Zlotnick, 55, an undeclared voter from Amherst, posed a hard question. Ms. Haley provided little by way of concrete policy proposals, but this time she drew an enthusiastic response.

A Question for Nikki Haley

“You said on TV that women who get abortions should not be put in jail and should not be subject to the death penalty. But how exactly should women who get illegal abortions — women like me — how do you specifically think we should be punished?”

The Subtext

Since the Supreme Court overturned Roe v. Wade, Republican-dominated state legislatures have rushed to institute new laws outlawing or imposing stringent restrictions on abortion, even as the issue has fueled Democratic victories across the nation, with Americans supporting at least some access to the procedure at record levels. Most abortions are now banned in 14 states. Some state laws stipulate narrow but vague exceptions, and carry years of prison time. Last week, a teenager in Nebraska who used abortion pills to end her pregnancy, and who pleaded guilty to illegally concealing human remains, was sentenced to 90 days in jail. At the time, abortion was banned in Nebraska after 20 weeks.

In the past, anti-abortion activists have largely maintained that they don’t support punishing women who seek out the procedure illegally. But more recently, some state lawmakers have proposed legislation with criminal consequences for patients as well as those who may help them.

Haley’s Answer

“In order for us to have a federal law, we’re going to have to have consensus. What does that consensus look like? Can’t we all agree that we don’t want late-term abortion? Can’t we all agree that we want to encourage more adoptions and good-quality adoption so that children feel more love, not less? Can’t we all agree that doctors and nurses who don’t believe in abortion shouldn’t have to perform them? Can’t we all agree that contraception should be accessible? And can’t we all agree that a woman who gets an abortion should not be subject to the death penalty or get arrested? That’s where I think we start — we start, and we do it with a level of respect. No more demonizing this issue. We’re going to humanize this issue. I had a roommate who was raped in college. I wouldn’t wish on anyone what she went through, wondering if she was OK. Everybody has a story. Let’s be respectful of everybody’s story, and let’s figure out what we can do together instead of sitting there and tearing each other apart.”

The Subtext

Ms. Haley began her reply by flatly stating that she did not believe women needed to be punished, adding that she was “unapologetically pro-life,” but did not “judge anyone for being pro-choice.” She went on to explain her support for the Supreme Court decision that thrust the issue back to the states but said she did see a role for the federal government in setting abortion policy, as long as there was congressional consensus between Republicans and Democrats.

Her answer mostly echoed her previous remarks on abortion, but delivered with passion, it seemed to pack a more powerful punch in front of a smaller, friendlier audience. Attendees nodded along or expressed whoops and hollers in agreement, breaking into applause as she ended.

Many Republican and independent women at her events this week have said they see Ms. Haley as a strong leader and messenger on abortion, as the only Republican woman in the presidential race, and believe she might be able to blunt attacks from Democrats on the issue. Ms. Haley’s positions on the topic tend to be more moderate than the rest of the field, and it is among the issues she has used to set up her bid as a test of the Republican Party’s attitudes about female leaders, without leaning too far into her gender.

After the event, Ms. Zlotnick, who once had to take a drug to end an unviable pregnancy — a procedure that is not illegal — said she phrased her question as a hypothetical because if she found herself in different circumstances, she would consider having an illegal abortion. She said she was a strong believer in reproductive rights but had been satisfied with Ms. Haley’s response.