Nikki Haley relishes boost in polling, fundraising as she pushes to break out from middle of GOP field

She was referred to by some voters as "Nikki who?" when running for governor of South Carolina -- and went on to become the first female minority governor in the country.

Now Nikki Haley has set her sights on becoming the first female president of the United States.

While she still trails Republican primary rival Donald Trump by double digits, and often still polls beneath 10%, like most of the rest of the crowded field, she's projected confidence about her staying power and has recently trumpeted some encouraging signs of gathering momentum.

"Get used to seeing this face," she'll say on the trail. Or: "Underestimate me, that'll be fun."

GOP voters say they are taking notice.

Political experts, too, see opportunity ahead for Haley but add that real challenges persist for the former U.N. ambassador -- a daughter of Indian immigrants and the only woman, as well as only non-white woman, to seek the 2024 Republican presidential nomination.

"Nikki Haley has a strong conservative record in South Carolina, but I think where she has a deficit right now is the fact that the other campaigns have war chests that she doesn't," said conservative political strategist Dave Wilson.

Haley's financial filings show she raised $7.3 million last quarter. Trump, by contrast, brought in more than $35 million through his joint fundraising entity.

After last month's primary debate, Haley said she managed to climb up in fundraising and volunteers and a poll released by CNN last week showed her as the only GOP presidential candidate beating President Joe Biden in a hypothetical head-to-head.

"I think the reason ... is simple," Haley said Sunday on CNN. "I think the majority of Americans know we need a new generational leader, that we need to leave the negativity of the past behind us. The majority of Americans don't want to see a rematch between Trump and Biden. That's been very clear."

A FiveThirtyEight/Washington Post/Ipsos survey of likely Republican voters, taken before and after the primary debate, also showed Haley gaining ground: She was ranked as doing the third best, behind only Florida Gov. Ron DeSantis and businessman Vivek Ramaswamy -- but fewer people also said she did the worst.

"What you saw on the debate stage is what I've done my entire life: I speak hard truths," Haley said afterward during a Parents for Nikki Town Hall in Manchester, New Hampshire.

Haley told Fox News that in the first 72 hours after the debate, her campaign raised $1 million and saw a massive jump in people wanting to get involved.

"We've had a fantastic response. I mean, truly ... We've had thousands of people volunteer, we've had a lot of people join the campaign, the phones are still ringing and so we're grateful. I mean, we're absolutely grateful but it only keeps us more motivated, because we have a country to save," she said.

Wilson, the strategist, said that "whenever you have a poll that comes through and shows a momentum growth, momentum begets momentum and always has. So this is an opportunity for Nikki Haley's supporters, and those who have been sitting on the fence waiting to see what's going to happen, to start coming up and funding her efforts moving forward."

"When you have money that you've raised, you have an ability to do things like advertising," Wilson said, adding, "Where Nikki Haley counters that is she's got a force in her message and her personality that we've been able to see, historically, has given her an ability to swing momentum in her direction, where money sometimes hasn't been there to do that."

Attendance at many of her stops on the trail has also gone up, with her first town hall after the debate, in South Carolina in late August, having standing room only and about 1,000 people in the main auditorium, balcony and overflow rooms.

New Hampshire resident David Osgood said he thinks Haley has been climbing since her debate performance and thinks she has positioned herself to become the next president, if she can win the GOP nomination and eat away at Trump's yawning lead among the base.

"I think she was the one that stood out the most," Osgood said of Haley's debate performance.

Some voters in Haley's home state agree.

"It's very exciting because she started out just barely registering on the polls and now she's really starting to take off," said Chris Richardson from South Carolina.

"I think her performance in the debate is a big part of that and you think that it's going to be really exciting as she moves forward," Richardson said.

Fellow South Carolinian Jason Jensen said "it's great that she's been so underestimated. Even when I first found out she was running for president, I didn't expect her to have the trajectory that she was going to have."

'You said some pretty harsh things about President Trump'

A potential sore spot for Haley in winning over conservative voters has been her comments about her former boss, including when she said Trump may have been "incredibly reckless" in his handling of classified documents. (He denies wrongdoing.)

"You said some pretty harsh things about President Trump on the debate stage. And so people are wondering if you were lying when you raised your hand to say he was supported," one voter said when he was picked for a question during a town hall in Claremont, New Hampshire.

Another said, "My feeling was that you didn't care for Trump and I understand that. I know he did a lot of good things for a guy that had nothing but opposition against him."

Haley defended her position.

"You know what I found interesting is people want me to love him 100% or they want me to hate him 100% of the time," she said during the town hall. "The media wants me to hate him 100% of the time. Trump supporters want me to love him 100% or something. I don't agree with anyone 100% of the time. So I'm always gonna be very, very honest in everything."

ABC News' Nicholas Kerr contributed to this report.