New Hampshire voters head to the polls on Tuesday for the first presidential primary of the 2024 nomination cycle, in a state that has been known to throw curveballs at overwhelming favorites.

The withdrawal of Gov. Ron DeSantis from the Republican race on Sunday effectively left what had recently been a crowded field of candidates down to two: former President Donald J. Trump, and former Gov. Nikki Haley of South Carolina.

The national Democratic Party, pushed by President Biden, had wanted New Hampshire Democrats to break tradition and move their primary to the end of February. New Hampshire refused, leaving the president’s supporters to mount a write-in campaign for the absent Mr. Biden against Representative Dean Phillips of Minnesota, the self-help author Marianne Williams and 19 other Democrats whose names are on the ballot.

After Mr. Trump trounced his opponents in the Iowa caucuses last Monday, here is what to watch on Tuesday:

After an early-January surge in the polls, Ms. Haley seemed be moving toward striking distance of Mr. Trump in New Hampshire, and when former Gov. Chris Christie of New Jersey dropped out on Jan. 10, it appeared that she briefly had a shot at consolidating the anti-Trump vote among Republicans, independents and about 4,000 Democrats who had re-registered as independent behind her.

New Hampshire polling in the last few days would indicate that any consolidation has fallen short of what she needs to win. If anything, Mr. Trump’s totals have inched upward. But New Hampshire has shocked the prognosticators before. Senator John McCain beat the overwhelming favorite of the establishment, George W. Bush, in 2000. Hillary Clinton bested a confident Barack Obama in 2008.

The viability of Ms. Haley’s candidacy might rest on an upset victory. The next big contest is in her home state, South Carolina, on Feb. 24. Mr. Trump holds a strong lead in the polls, but a win in New Hampshire could remind South Carolina Republicans why they voted for her twice to be their governor. A loss might be her Waterloo.

Since the Iowa caucuses rose to prominence in 1972, only six candidates have won both the caucuses and the New Hampshire primary in a contested race. Of those six, only Edmund Muskie, a Democratic senator from Maine, failed to capture his party’s nomination, and that was 52 years ago.

Mr. Trump’s hold on his party’s base may be more dominant than any of those previous two-state winners, and no presidential candidate in American history has had quite the same incentives to wrap up a nomination as quickly as possible. Facing 91 felony counts from four criminal cases, the former president wants to install ultra-loyal delegates to the Republican National Convention well before any of those cases go to trial, and certainly before a possible conviction might renew doubts about his fitness for the Republican nomination.

Just ahead of the Iowa caucuses, Mr. Christie dropped out in the hope that a stronger alternative to Mr. Trump could emerge. But it seemed too late. Mr. Trump’s landslide win there chased multiple candidates from the race, Vivek Ramaswamy, Asa Hutchinson, and ultimately, Mr. DeSantis, who had been hailed by Republicans early on as the strongest alternative to Mr. Trump in the race.

A convincing Trump win in New Hampshire, where independents had access to the Republican ballot, would leave Ms. Haley hobbled, with few states offering prospects nearly as attractive those in the Granite State. The monthlong slog toward the South Carolina primary, with few resources to draw from and a party clearly falling in line behind Mr. Trump could force her from the race as well.

Facing subzero temperatures and punishing winds, Iowa Republican voters largely gave last Monday’s caucuses a pass; just 110,298 showed up, compared with the 186,874 who voted in 2016, the last contested caucuses.

Snow showers are expected for New Hampshire, but temperatures could reach 40 degrees. State officials are predicting New Hampshire voters to set a turnout record. The New Hampshire secretary of state, David Scanlan, forecast voter turnout for the Republican primary will be 322,000, up from the record-setting 287,652 in 2016.

That would be a turnout of more than 60 percent of the total number of Republican and independent voters eligible to vote, compared with 18 percent of the eligible Republicans who showed up in Iowa.

For whoever wins, strong turnout could confer more legitimacy going into the long primary season. But Mr. Trump has for days raised doubts about the strength of Ms. Haley’s coalition, which he said will be dominated by independents and Democrats.

When Mr. Christie dropped from the presidential race, he said his decision was driven by his desire to do nothing that could help Mr. Trump return to the White House. But he didn’t endorse Ms. Haley, and on a hot mic, he told the world, “She’s going to get smoked,” doing her no favors.

That move was supposed to be “Donald Trump’s worst nightmare,” said John Sununu, a former New Hampshire Republican senator. It would turn the primary into a two-candidate race between the embattled former president and “someone who’s balanced budgets, who’s been a strong conservative leader and who, at the same time, hasn’t left chaos wherever she’s gone.”

No doubt many Christie voters have moved to Ms. Haley, though maybe not enough to put her over the top. But he didn’t campaign for her.

Then two days before the primary, another shoe dropped, or another candidate, Mr. DeSantis. In his case, he did endorse Mr. Trump and in a show of contempt for Ms. Haley, called her an old-guard candidate of vanquished Republican corporatism.

Suffolk University tracking polls of New Hampshire before Mr. DeSantis departed the race did not show many DeSantis voters available for any candidate; he had about 6 percent of the vote. But his parting shot at Ms. Haley may have sent those few to Mr. Trump. The Monday poll had the former president up 57 percent to 38 percent.

Tuesday will show whether Mr. DeSantis’s backing will help Mr. Trump leave her in the dust.

President Biden began his campaign for re-election determined to diminish the power of Iowa and New Hampshire in favor of states like South Carolina, Nevada and Michigan, with more racial, ethnic and economic diversity, which he saw as more representative of the Democratic Party.

Iowa Democrats acquiesced by changing their process. New Hampshire Democrats did not. Mr. Biden stuck to his guns.

So when Democrats go to their primary polling places, 21 Democrats will be on the ballot, but the president will not. A group of veteran New Hampshire Democrats are mounting a write-in campaign for Mr. Biden anyway, angry at how New Hampshire has been treated but determined not to elevate a long-shot alternative, such as Mr. Phillips or Ms. Williamson.

If it succeeds, perhaps the chatter of an alternative nominee to the 81-year-old incumbent could be silenced — at least for a while.

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