Nikki Haley’s presidential aspirations may hang on a victory in the New Hampshire primary election on Tuesday, powered by her sway with people who do not belong to a political party. It’s not a bad bet in a state where about 40 percent of voters call themselves independents.

The problem with her plan: Those voters come in all shapes and stripes, and many of them aren’t open to her.

Ms. Haley, the former governor of South Carolina, has won over plenty of voters in the middle in New Hampshire. They include moderate, conservative-leaning independents chased from the Republican Party by former President Donald J. Trump. And about 4,000 Democrats have re-registered as Republicans or independents to vote in the G.O.P. primary, in some cases to thwart Mr. Trump’s steady march to the nomination.

But New Hampshire’s potentially crucial primary will also include many other types of voters who have chosen to keep their distance from both parties:

  • Independents on the left who are loyal to their next-door senator, Bernie Sanders.

  • Independents on the right who plan to vote in the Democratic primary against President Biden.

  • True swing voters who are up for grabs in every election.

  • And working-class Trump supporters who don’t want to belong to a Republican Party long associated with the rich — but who are very much in the former president’s camp.

“Our country was thriving when he was in last time, so I’m going to go with what I know,” said Stacy Kolofoles of Laconia, who is a longtime independent but nonetheless “can’t see myself ever voting for a Democrat.”

Two dozen interviews with New Hampshire independents revealed stark challenges as well as ample opportunities for Ms. Haley as she courts the state’s largest political constituency. A new poll from Saint Anselm College spelled it out: Mr. Trump led Ms. Haley by 65 percent to 25 percent among likely Republican voters in the state, while she edged him among unaffiliated voters by a considerably narrower margin, 52 percent to 37 percent.

That 37 percent of independents for Mr. Trump may be decisive, however. Among all voters, he had a substantial advantage, 52 percent to 38 percent, and Gov. Ron DeSantis of Florida trailed far behind with 6 percent.

But the political quirkiness of the state’s independent voters means that it remains unpredictable how they will affect Tuesday’s results — and ultimately whether New Hampshire will slow or speed up Mr. Trump in the sprint to the nomination.

New Hampshire has one of the highest percentages of independent voter registration in the country, up there with Washington, Iowa and Colorado, according to an analysis of polling data by The New York Times. As of late December, 343,192 New Hampshire voters had registered as undeclared, while 262,262 were Democrats and 267,905 were Republicans.

And a large number of those independents are college-educated moderate voters, the kind who have gravitated to Ms. Haley, especially since former Gov. Chris Christie of New Jersey left the presidential race

Colin Carberry, 52, of Dover, is one of them. Mr. Carberry, who works in finance and lives in what he described as an affluent suburban neighborhood, voted for Mr. Trump in 2016, “and I’m not ashamed to admit my mistake.”

He will not do that again.

“He only cares about his own ego, empowering himself and his family at the expense of the country,” Mr. Carberry said.

He expects to vote for Ms. Haley but isn’t thrilled about it. He recalled being “taken aback” when she stumbled through an answer about the cause of the Civil War, neglecting to mention slavery, and he would have preferred that she shut down speculation that she might serve as Mr. Trump’s running mate.

His Dover neighbor, Joe Merullo, 68, who retired after 43 years with Sears to play bass in classic rock and party bands, has never registered with a political party. But, he said, he has also never voted for a Democrat for president, starting when he cast his ballot for Gerald Ford in 1976. He really wanted Mr. Christie, but without him in the race, Mr. Merullo said, he would vote for Ms. Haley with little enthusiasm.

A Trump-Biden general election would be even worse, he said.

“I don’t know what I’ll do, and it looks like I’ll be faced with that choice,” he said.

A lack of passion for Ms. Haley also surfaced in polls before Iowa’s caucuses.

The final Iowa Poll from The Des Moines Register, NBC News and Mediacom found that only 9 percent of her supporters said they were extremely enthusiastic to support her. The poll pointed to a narrow second-place finish for her, if she could rally her hesitant voters.

She didn’t, and fell to third place on Monday.

Such apprehension was evident in interviews with New Hampshire independents who were considering Ms. Haley.

David Fournier, 78, of Nashua, considers himself a lifelong Democrat and said he volunteered for the campaigns of Bill Clinton and Howard Dean. But he is not registered with a political party, he said, so he can keep the flexibility to vote in either party’s primary depending on the contest.

He is leaning toward casting a ballot for Ms. Haley, though he said he would “under no circumstances” support her in November should she win the nomination.

“It’s not a pro-Haley vote, it’s a negative-Trump vote,” Mr. Fournier said, adding, “Anything to put a ding on his belt.”

Several efforts are underway to engage undeclared voters in the primary. A new super PAC called Independents Moving the Needle on Wednesday began running two ads in New Hampshire featuring independent voters speaking directly to camera about their support for Ms. Haley. The group has booked more than $200,000 in airtime through Primary Day, according to AdImpact, a media tracking firm.

“This is about preserving our democracy, and there’s a man who is a threat to democracy,” said Robert Schwartz, who is leading another initiative to encourage voters — in particular, undeclared voters who participated in the 2020 Democratic primary — to vote in the Republican race this year against Mr. Trump.

If anything, the interviews were perhaps more heartening for Mr. Biden than for Ms. Haley.

New Hampshire has voted for Democratic presidential candidates since George W. Bush won the state in 2000.

But the state is still purple, with an all-Democratic congressional delegation but Republican control of the state legislature and governorship, thanks to independent voters like Kathleen Grindle Mack, 64, of Plainfield.

She has never voted for a Republican for president but has done so for governor, and she plans to back Ms. Haley next week, calling her the “least objectionable” option.

The prospect of a Biden-Trump rematch makes her want to “move to Canada,” she said, but she would probably vote for Mr. Biden, unless Ms. Haley won the Republican nomination.

“Trump scares me; Trump terrifies me,” she said. “When I was at the university, I studied European fascism, and he could have written the book on it.”

Bob Terrell, 82, a lifelong independent living in Goffstown, near the Uncanoonuc Mountains, voted for Mr. Trump in 2016. Now, he said, he thinks “Trump is a wacko.”

Then again, there are undeclared voters like Denyce Wallace, 57, of Concord. She supported Mr. Trump in 2020 and plans to do so again, saying she saw him as a man of action.

“I wish there were different candidates to choose from, maybe, but I’d rather have somebody who’s going to say something and then do it,” she said.

Of course, not all New Hampshire independents are deciding between Mr. Trump and Ms. Haley.

Joseph Lombardo, 73, of Windham, near the Massachusetts state line, considers himself independent, though he could not remember how he is registered. He was deciding this week between Mr. Trump and Mr. DeSantis.

“It doesn’t appear that he’s going to do anything different than what Trump did, so why not vote for the original?” he said of Mr. DeSantis.

Richard Bogart, 71, from Tamworth, voted for Mr. Trump in 2016 because, he said, the Democratic Party had not looked out for the “poor guy and the union guy.”

Mr. Biden won him back in 2020, and if Mr. Bogart votes in the primary on Tuesday, he will write in the president’s name, even though Mr. Biden will not be on the ballot, since New Hampshire Democrats did not abide by the party’s new primary order.

Mr. Bogart cited a hefty cost-of-living adjustment in Social Security benefits amid high inflation, and his fears that Republicans could roll back the program.

“Social Security, they’re always talking about doing away with it, and he gave me a raise,” he said of Mr. Biden. “That’s the best thing a president ever did for me personally.”

Ms. Haley clearly has many potential voters in the vast sea of independents, as evidenced by her rise in the polls to become more competitive with Mr. Trump.

“One thing I loved about Nikki Haley, she stood and said, ‘I’m not a lawyer, I’m an accountant,’” said Thomas Gross, a lifelong independent and retired Air Force officer who lives near Portsmouth. “Even though I’m in favor of many of the more liberal social issues, I realized that we need a good economy to provide funding for those issues, like pay for families with dependent children.”

Ms. Haley has to hope that the middle holds over the coming days, including people like Brian Smith, a 68-year-old engineer from Nashua who takes a dim view of both political parties or, as he called them, “the two political corporations.”

In 2020, he said, he wrote in “the most moderate person I could think of.” (He declined to share the name.) In 2024, he would write in a candidate again, perhaps Ms. Haley, if Mr. Trump and Mr. Biden were the two nominees.

But he had high hopes for Ms. Haley, who has his vote on Tuesday.

“Her stint in the United Nations has made her a lot more intelligent than I am in the political ramifications of world politics,” he said. “She did pretty well in her own state when she was there.”

He concluded, “She is not acting as extremist as the other people running in her party.”

Neil Vigdor and Ruth Igielnik contributed reporting.

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