Ambassador Nikki Haley returned to New Hampshire on Wednesday for a two-day blitz of town halls amid a surge in the polls in the first-in-the-nation primary state — but can she beat President Trump for the Republican nomination?

Recent polls show the former South Carolina governor and American ambassador to the United Nations closing the gap on Mr. Trump in the Granite State. An American Research Group poll released last week shows Ms. Haley trailing Mr. Trump by 4 percentage points in New Hampshire — the poll’s margin of error. Another recent poll from St. Anselm College, less encouraging for Ms. Haley, shows her with 30 percent support to Mr. Trump’s 44 percent.

Ms. Haley scored the coveted endorsement of the state’s popular Republican governor, Chris Sununu, earlier this month. Mr. Sununu, whose father was also a New Hampshire governor, won his fourth two-year term as governor in 2022 by more than 15 points. He is featured in a new Haley campaign ad that dropped this week, in which Mr. Sununu calls Ms. Haley “a leader who builds people up.”

“She’s a live free or die Republican who understands fiscal responsibility and individual liberty,” Mr. Sununu says in the ad. “She’s a new generation of conservative leadership, who can help leave behind the chaos and the drama of the past. We have an amazing opportunity. Let’s win with Nikki Haley.”

A libertarian conservative political advocacy organization backed by the Koch brothers, Americans for Prosperity, also endorsed Ms. Haley late last month. That endorsement brings considerable financial backing and a ground operation. The New Hampshire primary is on January 23, less than four weeks away.

Yet despite Ms. Haley’s surge in recent polls, Republican Party insiders in the state are cautious about making predictions. The air of inevitability around Mr. Trump looms large. At a holiday party this reporter attended last week outside Manchester with local Republican operatives, the buzz was that Ms. Haley is mounting a considerable challenge and will benefit from Mr. Sununu’s endorsement, but no one I spoke to was willing to put money on her winning the state.

That said, everyone agreed the race just got more exciting. “I think it is possible she can do this, but it’s still an upward challenge,” a former Trump administration appointee and Republican strategist in the Granite State, Matthew Bartlett, tells the Sun. “It’s not a crazy bet. If you’re going to put money on anybody else, that might be crazy. But right now, it’s not completely out of the question that she could do this.”

A consumer products consultant and member of the Bedford Republican Committee, Denis Cronin, tells the Sun why he is backing Ms. Haley: “She’s got incredible experience. She’s got executive experience as a governor. She has international experience at the United Nations. She’s mature. She’s smart.” Most importantly, he says, he wants a candidate who can beat President Biden, and polls show Ms. Haley has the most commanding lead in a head-to-head matchup.

 “She can bring in voters that wouldn’t vote for Trump,” Mr. Cronin tells the Sun. Yet he’s unsure she can win the Republican primary in his state, let alone others.

“Trump has the hardcore 30 percent or maybe more of primary voters, so the answer is I’m really not sure. But the answer is I think she could,” Mr. Cronin says.

Mr. Trump and other GOP presidential hopefuls are now attacking Ms. Haley as her star rises. On Truth Social, Mr. Trump decried the American Research Group poll as a “scam.” This comes amid reports that Mr. Trump is considering choosing Ms. Haley as his vice presidential pick, despite regularly insulting her.

“Fake New Hampshire poll was released on Birdbrain,” Mr. Trump posted, using his nickname for Ms. Haley. “Sununu now one of the least popular governors in U.S. Real poll to follow.”  

Governor Christie, who defended Ms. Haley against attacks by Governor DeSantis and candidate Vivek Ramaswamy in the last Republican debate, called Ms. Haley and his other rivals “Trump sycophants” on CNN. He says he is staying in the race because he is the only candidate willing to attack Mr. Trump.  

The DeSantis campaign created a “Trump-Nikki 2024” website that distorts the MAGA slogan to MEGA — “Make the Establishment Great Again!”

“For years, Nikki Haley has wanted to be Donald Trump’s Vice President,” the website says. “And now she is using her 2024 candidacy to finally make her VP dream a reality by following the lead of the former president as they’ve combined to spend over $30 million against Ron DeSantis, all while she refuses to attack Trump.”

Ms. Haley has been careful and pointed in her criticisms of Mr. Trump, recognizing that she needs to siphon votes from his base but not turn off his supporters. She says in her campaign stump speech that she agrees with many of his policies, and focuses her criticism on his divisiveness, penchant for drama, and advanced age. She always stays late to talk with voters at her campaign stops but rarely takes questions from reporters.

The recent polls that have Ms. Haley surging also show that much of her support is coming from New Hampshire’s “undeclared” voters, who can cast their ballots in either the state’s Republican or Democratic primary. At Haley campaign events the Sun has attended, many of her supporters say they will consider a No Labels or other third-party option if Mr. Trump wins the nomination.

One of Mr. Trump’s sons, Donald Trump Jr., told Newsmax he would oppose, and actively fight, his father picking Ms. Haley as his vice president, citing her disloyalty. Tucker Carlson and Steve Bannon have also said they will strongly oppose Ms. Haley on a Trump ticket.

“I wouldn’t have her and I would go to great lengths to make sure that that doesn’t happen,” Donald Trump Jr. told Newsmax’s Eric Bolling in a recent interview. “Nikki Haley wants never-ending wars. She’s a puppet of the establishment in Washington, DC.”

Mr. Bartlett says he doesn’t think Mr. Trump would seriously consider Ms. Haley as his running mate. “I don’t think he is a guy that will say, ‘You ran a great race against me, let’s bury the hatchet.’ I think he’s a guy that will bury the hatchet in your back or in your face.

“If she wins in New Hampshire, this will be one of the biggest shocks to the political presidential system ever. This is essentially defeating an incumbent president,” Mr. Bartlett says. Despite polls showing Mr. Trump winning decisively in other states — including Ms. Haley’s home state of South Carolina — Mr. Bartlett thinks a New Hampshire win could change the race.

“The entire eyes of the nation, the eyes of the world would then turn to Nikki Haley, millions would move off the sidelines overnight,” Mr. Bartlett says. “Let’s remember, Bill Clinton came in second in New Hampshire and declared himself the comeback kid — and the rest is history.”