The New Hampshire primary Tuesday will be a referendum on the direction of the Republican Party. Is this still President Trump’s party or do Republicans want to go in a new direction or perhaps to return to pre-Trump, George W. Bush-style leadership?

Nikki Haley represents the latter. The irony is that it will be New Hampshire’s independent voters, who make up the largest share — about 40 percent — of registered voters in the state, who will be the ones deciding this question. Undeclared voters can cast their ballots in either party’s primary in New Hampshire, and the secretary of state predicts record turnout on the Republican side.

As much as Governor Haley’s campaign is tempering expectations of a win in the Granite State, the primary this week is do-or-die for the Haley campaign. Mr. Trump earned more than 50 percent of the vote in Iowa, where Ms. Haley came in third. She must at least come in a close second to Mr. Trump in Tuesday’s contest, particularly now that Governor DeSantis has ended his own campaign.

A path to victory for Mrs. Haley will rely heavily on independent voters. New Hampshire is a last stand for Never Trumpers, Republicans who don’t like Mr. Trump, and independents who don’t want another Trump — or Biden — presidency.

“Is this the last stand or was there ever a stand?” a New Hampshire Republican strategist, Matthew Bartlett, tells the Sun. “There was always a notion from the Never Trumpers that if you could get this down to a one-on-one race between Trump and somebody else, he’d be finished. His ceiling is at 30 percent.”

“And now it appears, quite the opposite,” Mr. Bartlett adds. “The GOP is Maga Land.”

Polls indicate Mr. Trump will win in New Hampshire by about 14 points. The contest then moves to South Carolina, where Mrs. Haley was governor and where Mr. Trump is polling 30 points ahead of her. Yet some Granite State politicos say it’s too early to count Mrs. Haley out.

“This state is very hard to poll,” the director of the New Hampshire Institute of Politics, Neil Levesque, tells the Sun. “New Hampshire can turn on a dime and can surprise people.”

Mr. Levesque points to George H.W. Bush, who came in third in Iowa, only to eke out a win in the Granite State and onward to the presidency. He mentions Hillary Clinton, who was polling behind Barrack Obama after losing in Iowa, but managed to win the Granite State in 2008.

“We’ll see whether or not it’s too late, or whether or not the lock and glue that Trump has with so many Republican voters holds true,” Mr. Levesque says.

Ms. Haley, flanked on the trail by the Granite State’s governor, Chris Sununu, has stepped up her campaign in recent days. She did six events on Sunday and five on Monday. She has also stepped up her attacks on Mr. Trump, questioning his mental acuity at a campaign rally in Peterborough Saturday and calling out Mr. Trump for his “bromance” with Vladimir Putin, Xi Jinping, and Kim Jong Un.

The director of the University of Virginia Center for Politics, Larry Sabato, said on CNN, “It is definitely too little, too late.”

“It’s all about getting out the vote,” Mr. Sununu told an audience in Exeter Sunday night at a school auditorium filled to its 1,000-person capacity. “If you’re going to sit and complain that democracy is threatened, then don’t sit on the couch on Tuesday and wait for someone else to do the job.”

The campaign seemed to be having fun at the Exeter rally, where Judge Judy introduced Ms. Haley as the “next president of the United States.” Campaign volunteers threw t-shirts and swag to the crowd like it was a rock concert.

Yet despite the packed auditorium, if this were a Trump rally, the crowd size would be called anemic. Mr. Trump held a stadium rally in Manchester Saturday night with thousands in attendance. He’s held rallies every night for the past few days. Each night, crowds have lined up in the cold hours to get a seat.

“It’s comedy and inspiration all at once. It’s like church,” a Trump volunteer at the campaign headquarters in Manchester, Caroline Gagan, tells the Sun Saturday about Mr. Trump’s speeches.

Ms. Haley’s supporters, though, are holding out hope. “I think it’s going to be much closer than people realize,” a former member of Chris Christie’s steering committee, Tom Boucher, who left last month to endorse Ms. Haley, tells the Sun.

Mr. Boucher hosted a Haley event at one of his restaurants Monday. “Undeclareds are going to make all the difference,” he says.

“I’m hopeful for Tuesday but I’m also scared,” an undeclared voter at a Haley campaign stop on Saturday, Julie Lombardozzi, tells the Sun. “I’m just afraid Trump is going to take the lead on Tuesday no matter what she does. He’s just that far ahead.”

“I don’t think she’s going to make it, but you’ve got to try,” another undeclared voter, David Petty, tells the Sun.

Mr. Levesque says Mr. Trump’s dominance in the polls could impact turnout for Ms. Haley. “Polling always influences voters because they have to get in the car and drive to the polling spot and potentially vote for someone who the obituary is being written for,” he says.

“It’s a very interesting time in American politics, where you have two parties with bases that are like glue to their nominee,” Mr. Bartlett says. “And it seems that the rest of the country is nowhere near enthusiastic about either one.”