UPDATE 4-Haley seeks upset in New Hampshire, Trump confident of big win

(Adds exit polls, paragraphs 7-8)

By Gram Slattery, James Oliphant and Nathan Layne

MANCHESTER, New Hampshire, Jan 23 (Reuters) - Nikki Haley looked to New Hampshire voters on Tuesday to keep her White House hopes alive by slowing Donald Trump's march to the Republican presidential nomination and scoring enough support to keep her campaign going in bigger U.S. states.

The former U.S. president and Haley, a former South Carolina governor who was Trump's ambassador to the United Nations, were in a two-person race in the New England state after Ron DeSantis, the Florida governor, dropped out and endorsed Trump.

Opinion polls show Trump with a wide lead over Haley, who needs a victory or at least a strong showing in New Hampshire to carry her to the next nominating contest in her home state, where Trump is also dominant in the polls.

Trump had a record-setting victory in Iowa's first-in-the-nation contest last week.

A resounding win in New Hampshire would help propel Trump to secure the party's nomination despite multiple criminal counts against him, two impeachments and his chaotic 2017-2021 presidency.

The Republican nominee will face President Joe Biden, the presumptive Democratic nominee, in the general election in November.

The first exit polls in New Hampshire showed 69% of Republican primary voters said the economy was either poor or not good, an area where Biden has struggled to highlight improvements during his administration.

The exit polls also showed that 49% of New Hampshire primary voters do not think Biden legitimately won the 2020 presidential election, a false claim perpetuated by Trump since he lost it. Fifty percent of them said Trump would still be fit for the presidency if convicted of a crime.

Trump, who is balancing campaign stops with appearances in various courts, denies wrongdoing and has used the criminal charges to bolster his claim of political persecution.

He predicted victory in New Hampshire early on Tuesday, saying the level of enthusiasm was incredible. Later, during a stop at a polling station in Londonderry, Trump briefly addressed supporters.

"So excited. I'm very confident," he said.

The first ballots in New Hampshire went to Haley. Voters in the tiny northern hamlet of Dixville Notch - always the first to vote in the state - chose Haley over Trump 6-0.

New Hampshire, while also a mostly white state with a small population, has a more moderate Republican electorate and a better record of predicting the eventual nominee.

Haley came in a close third behind DeSantis in Iowa and has focused her early campaign on New Hampshire.

"It's a building game," she said in Manchester. "You just want to keep getting stronger and stronger and stronger. That's our goal."

Haley's campaign said on Tuesday it intends to keep her candidacy alive through "Super Tuesday" in early March, when 16 states vote.

"After Super Tuesday, we will have a very good picture of where this race stands. At that point, millions of Americans in 26 states and territories will have voted," a campaign memo said.

DEMOCRATS' STRATEGY

Biden is not on the ballot in New Hampshire's Democratic primary, having supported an effort by his party to move their first primary election to the more diverse state of South Carolina.

New Hampshire supporters will still be able to vote for him by writing Biden's name on the ballot, which could be a barometer of his political strength.

The Democratic president, whose advisers are anticipating a rematch with Trump, planned a rally in Virginia on Tuesday night to discuss the threat to abortion rights if Republicans win back the White House.

Democrats in Virginia secured majorities in the state legislature after making abortion rights a central campaign issue.

The Supreme Court, with a conservative majority made possible by three justices who joined the court under Trump, struck down in 2022 the Roe vs Wade ruling that guaranteed women's right to abortion.

Biden, in addition to focusing on abortion, has cast Trump as a would-be dictator and a threat to democracy.

In New Hampshire, Haley stepped up her attacks on Trump, criticizing his affinity for strongmen such as Russia's Vladimir Putin and North Korea's Kim Jong Un.

Haley, 52, has also gone after Trump's age - he is 77 - and mental acuity, attacks she has also regularly leveled at Biden, who is 81.

She took up the theme again on Tuesday, saying the country needs to put someone in the White House that can put in eight years to get it back on track.

"Do you want two 80-year-olds running for president?" Haley asked.

In Manchester, voter Don Salem said he didn't think people on either side wanted a Biden-Trump contest. Yet he backed Trump in 2020 and voted for him again on Tuesday.

"There's been a lot of attacks on him, but I've ignored that for the most part," Salem said. (Reporting by Gram Slattery, James Oliphant and Nathan Layne; Additional reporting by Jane Ross and Kia Johnson in New Hampshire; Writing by Jeff Mason and Doina Chiacu; Editing by Kieran Murray, Alistair Bell and Howard Goller)