Nikki Haley, in her final appearances before polls close in New Hampshire Tuesday night, rejected claims that Republican voters had already solidly united behind former President Donald J. Trump, and pledged not to end her 2024 presidential bid no matter how the state’s first-in-the-nation primary turned out.

“I didn’t get here because of luck,” she said at a polling site in Hampton, N.H., while flanked by supporters, including Gov. Chris Sununu, her top surrogate in the state. “I got here because I outworked and outsmarted all the rest of those fellas. So I’m running against Donald Trump, and I’m not going to talk about an obituary.”

Asked for her response to Mr. Trump’s remarks at his rally a day earlier, in which he suggested she would likely drop out after New Hampshire, she smiled.

“I don’t do what he tells me to do,” she said. “I’ve never done what he tells me.”

In her closing pitch to voters, Ms. Haley, the former governor of South Carolina and a United Nations ambassador under Mr. Trump, has cast herself as an underdog who has come from behind before and is willing to take on her own party’s political class. Her supporters and allies have projected confidence.

“I’m not worried because I’ve seen this movie before,” Katon Dawson, a former chairman of the South Carolina Republican Party who now serves as an adviser to the Haley campaign in that state, said in an interview.

But the forces that carried her to the Governor’s Mansion as a deeply conservative and anti-establishment Tea Party candidate in 2010 are now squarely behind Mr. Trump, and the former president has remade the Republican Party in his image.

Polls continue to show his dominance in New Hampshire and nationally. The latest Suffolk University/NBC10 Boston/Boston Globe tracking poll found that he had only expanded his lead in the state since Gov. Ron DeSantis of Florida suspended his presidential campaign on Sunday. The survey showed Mr. Trump with 60 percent of support from voters, while Ms. Haley had 38 percent. (The margin of error was 4.4 percent.)

During his own visit to a polling site on Tuesday, Mr. Trump dismissed the idea that Ms. Haley posed a threat to his march toward the nomination. “She can stay in,” he said of her campaign’s memo stating that she would not be dissuaded from fighting on.

On Tuesday, Ms. Haley was expected to visit a couple of polling locations before her watch party at her state headquarters in Concord, N.H.

At Winnacunnet High School in Hampton, N.H., her first site visit on Tuesday morning, at least a half-dozen signs at the entrance promoted Mr. Trump and appeared to be digs at Ms. Haley, including ones that read “Secure Borders” and “No Wars.” His campaign has been painting her as a warmonger and attacking her record as governor, particularly on immigration. Most of the volunteers standing outside and pumping up voters were from the Trump and Biden campaigns.

Ms. Haley arrived at the high school with her own calvary. Her supporters engaged in a battle of chants with the Trump campaign, as competing shouts of “Trump, Trump” and “Nikki, Nikki” filled the air. On hand were her two main surrogates in the state, Mr. Sununu and Don Bolduc, a retired Army brigadier general who unsuccessfully ran for the Senate in 2022.

In a news conference, Ms. Haley rejected claims that Mr. Trump had put her campaign on the defensive in the crucial last days of the race. But just days after sharply questioning the former president’s mental acuity, she once more declared him “mentally fit.” “The problem is do you want two 80-year-olds running for president?” she asked.

She argued that it was not Republican voters rallying behind the former president, but her party’s “political elite.”

“That’s not what Americans want,” she said of a second Trump presidency. “The political class has gotten us into this mess.”

Ms. Haley and Mr. Sununu pointed to her sweep in the midnight primary of Dixville Notch, N.H. (where she took all six registered voters) and predictions of record turnout as harbingers of a strong performance today. But even if she does not win New Hampshire, Ms. Haley told reporters, she plans to move on to South Carolina, her home state, where her campaign has already placed an ad buy.

“This has always been a marathon,” she said. “It’s never been a sprint.”

Leaving the polling site in Hampton, N.H., Daniel Hamilton, 67, a former business controller who described himself as a moderate Republican, echoed Ms. Haley’s sentiments, saying he did not want four more years of either President Biden or Mr. Trump.

“I think she’d do a good job,” Mr. Hamilton said. “She is qualified, and I want to move on from the Biden-Trump deal.”

Michael Gold contributed reporting.

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