A new WBUR poll (topline, crosstabs) shows Hillary Clinton leads Donald Trump by 7 points among likely voters in New Hampshire, one of the key battleground states that could determine the outcome of the presidential election.

The survey also found that by a wide margin, voters believe Clinton was the clear winner in Monday night's debate against Trump.

The live telephone poll of 502 likely voters was conducted Sept. 27-29. It has a margin of error of 4.4 percentage points.

The new survey is in line with a number of national and battleground state polls that have come out since Monday night's debate. They suggest that after watching her sizable post-convention lead over Trump all but disappear, Clinton has put the brakes on her fall and has gained some ground. According to the WBUR poll, in New Hampshire, she now leads Trump 42 to 35 percent.

"She had what appeared to be a very good performance -- voters rated it very positively in the debates," says Steve Koczela, president of the MassINC Polling Group, which conducted the WBUR survey. "And she seems to have stopped the slide that she was experiencing going into the debate."

Koczela says, by a three to one margin, New Hampshire voters say Clinton won the debate.

But consistent with previous polls, this one identified a big challenge that both candidates continue to struggle with: Neither of them is very well liked. Fifty-one percent of voters have a negative view of Clinton; 61 percent feel that way about Trump.

The poll also found that Clinton continues to build a striking advantage among women. Almost half of them view her favorably. And according to Koczela, a whopping 70 percent of women view Trump unfavorably.

"That translates into votes," Koczela says. "You know, there's going to be a big gender gap, but it's the size of the gender gap I think that makes a difference. And when you see these numbers, how few women view him favorably, I think that's a real concern for him."

And it's an advantage that Clinton was eager to press at the debate on Monday.

"This is a man who has called women pigs, slobs and dogs," Clinton said during the debate, "and someone who has said pregnancy is an inconvenience to employers, who has said women don't deserve equal pay unless they do as good a job as men."

If Clinton has a large advantage among women in New Hampshire, Trump has a smaller, but still substantial, advantage among men. According to the poll, they favor him by nine points more than they favor Clinton.

"I'm voting for Trump," said 20-year-old Josiah Adams of Greenfield, New Hampshire. Adams says he will be voting in his first presidential election next month.

"He's like definitely more for the people," Adams says. "Hillary, like, she's been in politics for so long. I mean, how she's been able to make all the money she has just being in politics, it just kind of says a lot about her. And Trump seems like a way better choice."

Adams says he watched the debate Monday night, and felt Trump did pretty well at the beginning, but then faded. But he says it really didn't change his view of the candidate.

"I want to see him do better in the next ones," Adams says, "but, honestly, I'm not sure how much the debates even really persuade people. I think at this point a lot of people have already made up their minds."

That view was borne out by the WBUR poll. It found that most people say the debate didn't influence how they regard the candidates. But about a quarter said Clinton's performance would make them more likely to vote for her, while roughly the same number said Trump's performance would make them less likely to vote for him. So, advantage Clinton.

On the question of which candidate is fit to be president, the poll identified another big advantage for Clinton: About half of those surveyed say Clinton is qualified. Only a third say Trump is. And many Republicans — a third of them, in fact — say he's not.

"That number really hasn't changed a lot since we polled over the summer — that he's not fit to be president," Koczela says. "But the fact the even his own partisans aren't necessarily sold on the idea, I think is quite remarkable."

At a Clinton rally this week on college affordability at the University of New Hampshire, plenty of people said Trump is unfit to be president. Among them was Eli Tyrrel-Walker, a student at UNH who supports Clinton, and is exactly the kind of young voter she needs to win over.

"To be honest, I was a Bernie [Sanders] supporter, and a pretty big one," Tyrrel-Walker said. "And then our democracy spoke and Hillary won, and I had no problem switching. I never had many problems with her, even when I supported Bernie. I love this event because she's coming to the college, speaking to students about issues that are concerning them."

With less than six weeks to go until election day, the WBUR poll found that most voters have made up their minds, with just 4 percent still undecided. In a tight race, they could prove decisive — meaning it could come down to voters like Dave Tremblay of Hillsborough, New Hampshire.

"Well, it's hard because I really don't want to vote for Hillary," Tremblay says.

Tremblay was a Sanders supporter because he says he wanted to vote for change. Now he's considering Trump but says he's still undecided.

"Hillary is just not going to bring a lot of change — not that I agree with everything with Trump," Tremblay says.

Another option for Tremblay is Libertarian candidate Gary Johnson, who's favored by 13 percent of New Hampshire voters, according to the poll.

Editor's Note: An earlier version of this story mistakenly included a quotation from a Clinton supporter that was gathered in August. We regret the error.