Atkinson, N.H. — After Donald Trump’s record victory in the Iowa caucuses, New Hampshire voters now get their turn to decide just how competitive the Republican nominating fight will be as the former president continues to dominate his party.

Trump was eager Tuesday to flaunt his 30-point victory in Iowa a night earlier, as he stepped up the pressure on former U.N. Ambassador Nikki Haley and Florida Gov. Ron DeSantis to improve on their distant finishes in the opening votes of the 2024 presidential election. They have a one-week sprint ahead of next Tuesday’s primary in New Hampshire, the longtime host of the nation’s first Republican presidential primary.

“Our country is dying. ... And I stand before you today as the only candidate who is up to the task of saving America,” Trump declared in Atkinson, where hundreds of his supporters cheered the former president's boasts about his standing in polls, attacks on President Joe Biden and sweeping promises to “make our country rich as hell again.”

DeSantis, the Florida governor, and Haley, Trump's former United Nations Ambassador and onetime South Carolina governor, were campaigning Tuesday in New Hampshire, as well. DeSantis got about 21% of the vote in Iowa, 30 percentage points behind Trump’s narrow majority and 2 points ahead of Haley’s third-place finish.

New Hampshire's electorate is less religiously conservative and less rural than in Iowa, factors that helped Trump in the caucuses. If DeSantis and Haley cannot capitalize on those differences, they could watch Trump sustain momentum that would render the rest of the Republican primary calendar little more than a formality.

“You must go out and vote,” Trump said. “We have to show margins like never before.”

Haley, who has sought to build a wide coalition that includes independents, has put great emphasis on New Hampshire, hoping it becomes a springboard to her home-state South Carolina primary next month. DeSantis, who has run more as a Trumpian conservative, put more stock in Iowa, so now must regroup quickly for New Hampshire or risk squandering his second-place finish.

Severe winter weather already is altering campaign schedules and making their tasks harder. DeSantis's campaign had to cancel an afternoon event because of difficult travel conditions.

ABC News, meanwhile, canceled a Thursday debate after it became clear only DeSantis seemed sure to participate. Haley, angling to frame the primary as a battle between Trump and herself, had suggested earlier Tuesday that she would debate only if Trump joined her. Trump has skipped every GOP primary debate so far and said he would take the stage only against a Republican rival who was commensurate with him in the polls.

“We are beating everybody,” Trump bragged in Atkinson, where he also showed off an endorsement from Vivek Ramaswamy, the biotech entrepreneur who suspended his campaign after finishing with single-digit support in Iowa. Ramaswamy joined Trump on stage and pledged to help him win in November.

Texas Sen. Ted Cruz, who defeated Trump in the Iowa caucuses in 2016, endorsed the former president Tuesday evening, as well. “At this point, I believe this race is over so I'm proud to endorse Donald Trump,” Cruz said on Fox. News.

Former Arkansas Gov. Asa Hutchison, a harsh Trump critic, also suspended his bid Tuesday, leaving a three-candidate field. Hutchison pointedly did not endorse Trump.

Trump began his day in New York, appearing at a civil defamation trial stemming from a columnist’s claims he sexually attacked her, but used his legal troubles, including four pending criminal cases against him, as part of his pitch, dismissing “bullsh— indictments” as a Biden administration effort to derail his political comeback.

Certainly, Trump's troubles have given some Republicans pause and turned off plenty of independents. According to an APVoteCast survey of more than 1,500 Iowa caucusgoers, about a quarter of caucus participants believe Trump has done something illegal when it comes to at least one of the legal cases he is facing: his role in the Jan. 6, 2021, riot at the U.S. Capitol, his alleged attempts to interfere in the vote count in the 2020 presidential election or the discovery of classified documents at his Florida home that were supposed to be in government custody.

Kristen Mansharamani, an independent voter from Lincoln, New Hampshire, said she has never considered backing Trump in 2024 and would back Haley.

“I told my 12-year-old son that I am looking for the person who I think is going to get rid of some of the standstill and the polarization in politics and I think she can do that better than anyone else out there right now,” the 48-year-old said.

Yet Haley and DeSantis must contend with hardcore Republicans like Nancy Otovic, a 75-year-old retiree who stood in frigid conditions for hours Tuesday to hear Trump.

“Our world is in a spiral, and he's going to help us,” she said, her parka still wet even after she made it indoors. Enduring subfreezing weather, she said, was a necessary sacrifice to see the former president. “Happy to be here,” she declared.

The question is whether the electorate next Tuesday has enough voters like Mansharamani. Voters who are registered without a party affiliation make up about 40% of the electorate in New Hampshire and are eligible to cast a Republican primary ballot. New voters can also register at the polls on Tuesday.

Haley leaned directly into New Hampshire’s reputation for independence, launching a statewide television ad Tuesday morning that hit both Trump and Democratic President Joe Biden ahead of her arrival in the state.

“The two most disliked politicians in America,” the ad calls them, painting the 81-year-old president and 77-year-old former president together as being “consumed by chaos, negativity and grievance of the past.”

DeSantis, meanwhile, opted to start in Haley's home state, where he attacked her rather than Trump. In Greenville, South Carolina, DeSantis dismissed Haley’s attempts to frame the campaign as a battle between her and Trump. DeSantis panned Haley’s performance as governor and said his Florida record earned more support from Iowa conservatives.

As for Trump, DeSantis acknowledged the former president’s advantage, calling him “basically an incumbent,” while at the same time trying to minimize his victory margin in Iowa.

“Half the people wanted someone else,” DeSantis said. Trump, in fact, stood at 51% with 99% of the vote counted, well outpacing Haley's and DeSantis' combined vote totals.

Haley’s and DeSantis’ tacks coming out of Iowa nonetheless reflect the support they drew in the caucuses.

According to AP VoteCast data that surveyed more than 1,500 caucus participants, Haley was the top candidate of the most anti-Trump Republicans in Iowa, including those who believe the former president did something illegal in one of the pending criminal cases against him. She was also the top choice for those who voted for Biden in the 2020 election.

In total, less than half of her supporters in Iowa said they voted for Trump in 2020, with the remainder supporting Biden, saying they supported a third-party candidate or that they stayed home.

DeSantis, meanwhile, performed best among the caucusgoers dissatisfied with Trump but who said they would ultimately vote for him in the general election. Most Iowa caucusgoers for either Haley or DeSantis say they would be dissatisfied with Trump as their party’s nominee. But unlike DeSantis’ backers, two-thirds of Haley’s caucusgoers say they would not ultimately vote for Trump in the general election.

If there is an opening for DeSantis and Haley, it could be forecast in Trump’s weakness in the Iowa suburbs, where he won only a third of the votes. Iowa’s suburbs are more educated and less evangelical than the state’s rural and small-town areas Trump dominated. New Hampshire’s Republican electorate is more reflective of Iowa’s suburban population.

Barrow reported from Atlanta and Price reported from Atkinson, N.H. AP Director of Public Opinion Research Emily Swanson in Washington and Jeffrey Collins in Greenville, S.C., contributed.