Haley waves to the audience as she speaks at a New Hampshire primary night rally, in Concord, New Hampshire, on Tuesday, January 23. (Charles Krupa/AP)

(CNN) โ€” Former President Donald Trump took a huge step toward winning a third consecutive Republican presidential nomination Tuesday, winning the New Hampshire primary in a one-on-one matchup with his last challenger standing, former South Carolina Gov. Nikki Haley.

Haley vowed to remain in the Republican race, saying sheโ€™ll now focus on the February 24 primary in her home state of South Carolina.

But sheโ€™ll be battling history: In modern presidential campaign history, no non-incumbent has won the Iowa caucuses and New Hampshire primary without going on to win his partyโ€™s nomination.

Trump, who took the stage shortly after Haley spoke, seethed over her decision to continue her campaign.

โ€œShe had to win,โ€ the former president said. โ€œShe failed badly.โ€

As Haley seeks to prove she remains a viable contender, President Joe Biden began preparations for a general election rematch with Trump โ€” dispatching senior White House staffers to work on his campaign and holding an event in Virginia where he hammered Trump on abortion rights.

Here are five takeaways from the New Hampshire primaries:

Trump wants Haley out โ€” now

In what were expected to be celebratory remarks Tuesday night in New Hampshire, Trump instead sounded annoyed that Haley had not yet dropped out of the Republican primary race.

He mocked Haley, calling her an โ€œimposterโ€ who had โ€œclaimed victoryโ€ despite doing โ€œvery poorly.โ€ (Haley, in fact, had congratulated Trump for his victory at the beginning of her remarks.)

His remarks made plain that Haleyโ€™s attacks on Trumpโ€™s age, his verbal miscues and Republican losses during his time as the partyโ€™s leader have frustrated the former president.

It was a jarring contrast from Trumpโ€™s election night remarks eight days ago in Iowa, when he praised his rivals as โ€œvery smart people, very capable peopleโ€ and predicted that Republicans are โ€œgoing to come together. Itโ€™s going to happen soon, too.โ€

He invited two former 2024 GOP contenders, entrepreneur Vivek Ramaswamy and South Carolina Sen. Tim Scott, to attack Haley on stage Tuesday night.

โ€œWhat we see right now with her continuing in the race is the ugly underbelly of American politics,โ€ Ramaswamy said, blaming Haleyโ€™s decision to continue her candidacy on โ€œmegadonorsโ€ who are out of step with what Americans want. โ€œWhat we saw tonight is America first defeating America last.โ€

Later, he gave Scott, who stood on stage behind him days after endorsing the former president, the chance to jab at Haley. He noted that Haley had appointed the South Carolina Republican to the Senate in 2013.

โ€œDid you ever think that she actually appointed you, Tim?โ€ Trump said. โ€œYou must really hate her.โ€

Scott diplomatically stepped to the microphone to interject. โ€œI just love you,โ€ he said.

Haley says GOP race is โ€˜far from overโ€™

Though Trump is eager to move past the Republican primary, and Bidenโ€™s campaign manager Julie Chavez Rodriguez said Tuesday night that Trump โ€œhas all but locked upโ€ his partyโ€™s nomination, Haley insisted she wonโ€™t leave the race.

โ€œNew Hampshire is first in the nation. It is not the last in the nation. This race is far from over. There are dozens of states left to go,โ€ Haley told supporters in her election night speech Tuesday in New Hampshire.

Whatโ€™s not clear, though, is where Haley could actually notch a victory against Trump. She isnโ€™t participating in the Nevada caucuses on February 8 (she will instead be on the stateโ€™s primary ballot, which wonโ€™t lead to her winning any delegates), and polls in her home state of South Carolina โ€” where the February 24 primary will be the next major showdown โ€” show Trump with a huge lead.

Haley is likely to face immense pressure to depart the race in coming days. Sheโ€™ll face questions about whether sheโ€™ll follow a path similar to Florida Gov. Ron DeSantis, who vowed to continue on after his second-place finish in last weekโ€™s Iowa caucuses โ€” and then he dropped out days later.

Haleyโ€™s campaign said Tuesday it is placing $4 million in television advertising reservations in South Carolina. She has also scheduled a rally Wednesday night in North Charleston.

Mark Harris, executive director of the pro-Haley super PAC SFA Fund, told CNN the group is โ€œon to South Carolinaโ€ and plan to spend millions on ads, mail and more.

Haleyโ€™s argument: Trump is a loser

Haley used her Tuesday night speech to make her most pointed argument yet about electability โ€” blaming Trump for Republicansโ€™ disappointing performances in the 2018 and 2022 midterms and the 2020 presidential election.

โ€œWith Donald Trump, Republicans have lost almost every competitive election,โ€ she said, ticking through GOP failures during Trumpโ€™s time as the partyโ€™s leader. โ€œThe worst-kept secret in politics is how badly the Democrats want to run against Donald Trump.โ€

A supporter shouted: โ€œHeโ€™s a loser!โ€

The former South Carolina governor called Trump โ€œthe only Republican in the country who Joe Biden can defeat.โ€

She also highlighted their ages. Trump will be 78 on Election Day in November; Biden will be 81. She also questioned Trumpโ€™s mental competency, and challenged him to debate her. (Trump skipped all five Republican primary debates, and has shown no indication heโ€™d consider participating in one.)

Trump is dominating Republican primary polls. But polls also show Haley outperforms the former president in a hypothetical general election matchup with Biden โ€” something Haley has frequently noted in recent days.

โ€œThe first party to retire its 80-year-old candidate is going to be the party that wins this election,โ€ she said Tuesday night. โ€œAnd I think it should be the Republicans that win this election. So our fight is not over, because we have a country to save.โ€

Warning signs for Trump

Though Trumpโ€™s win was a huge step toward cementing the GOP nomination, there were warning signs for his general election hopes within CNNโ€™s exit polls of New Hampshire Republican primary voters.

Haley won the 29% of the electorate that identified themselves as moderate by a 3-to-1 margin.

On the issue of abortion, Trump was the strong favorite of those who support banning most or all abortions nationwide, but Haley edged him out among the 67% of the primary electorate that said they would oppose a ban. Bidenโ€™s campaign on Tuesday signaled its intent to make abortion rights a central focus of the general election.

โ€œLet there be no mistake: The person most responsible for taking away this freedom in America is Donald Trump,โ€ Biden told supporters at a rally in Manassas, Virginia.

There were other potential signs of trouble with moderate voters for Trump. Among them: 44% of the primary electorate said Trump is not fit for the presidency if he is convicted of a crime, and Haley won 84% of those voters. Haley won 79% of the votes of those who said Biden legitimately won the 2020 election โ€” showing a potentially limited appetite among voters for Trumpโ€™s lies about widespread election fraud.

President Joe Biden delivers remarks during a campaign event focusing on abortion rights at the Hylton Performing Arts Center, in Manassas, Virginia, on Tuesday, January 23. (Evelyn Hockstein/Reuters)

Bidenโ€™s general election bid takes shape

Biden won the New Hampshire primary on Tuesday night, but he had been at risk for blowback in New Hampshire after he led the Democratic push to demote the state in the partyโ€™s nominating process โ€” elevating South Carolinaโ€™s primary to become the first contest with delegates on the line.

The Democratic National Committee had called the vote โ€œmeaninglessโ€ and had urged presidential candidates to โ€œtake all steps possible not to participate.โ€ Still, Bidenโ€™s allies launched a low-key effort to get Democrats to write in Biden, and it paid off with an easy victory.

It was a reminder that even though Minnesota Rep. Dean Phillips and author Marianne Williamson are challenging Biden, there is no drama: Bidenโ€™s path to the Democratic nomination for a second term is clear.

Bidenโ€™s campaign, meanwhile, is preparing for an early start of the general election, moving two senior aides from the White House to his reelection campaign in Wilmington. Jen Oโ€™Malley Dillon, who was campaign manager for Bidenโ€™s 2020 campaign, is poised to transition to a role as Bidenโ€™s campaign chair, while Mike Donilon, a long-time Biden messaging guru, will be chief strategist.