Concord, New Hampshire - Nikki Haley surged again on Tuesday in new polls of the Republican presidential primary and has cut former president Donald Trump's lead to single digits in New Hampshire, new surveys revealed.

Haley scored 32% compared to 39% for Trump in a new CNN survey of Granite State voters, with rival Ron DeSantis languishing in fifth place with 5%.

A separate poll of voters in Iowa, where the GOP caucus kicks off the voting on Monday, showed Haley and DeSantis locked in a virtual tie with about 15% support, far behind Trump who scored 51%.

Haley pitched herself as having an unrivaled ability to win over independents and moderates in a general election battle with President Joe Biden.

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"We need a candidate who can leave the negativity and the baggage in the past and go forward with solutions for the future," Haley told supporters in suburban Des Moines.

As the former UN ambassador prepares for a final debate set for Wednesday with DeSantis, the new surveys mostly reflected Haley's continuing momentum in the race, where her standing has risen in polls for several months.

She remains far behind Trump overall, who remains the favorite to capture the nomination.

A second poll of New Hampshire gave a somewhat different picture of the race with Trump leading Haley by nearly 20% in that survey conducted by USA Today and the Boston Globe.

Haley hopes to finish ahead or about even with DeSantis in Iowa, a potentially devastating blow to the Florida governor who has spent months wooing the Hawkeye State and its dominant evangelical Christian conservative voting bloc.

The former South Carolina governor could potentially ride into a virtual one-on-one matchup with Trump in New Hampshire, where political independents can vote and could give her a big leg up.

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That scenario would put Haley in the position to scramble the race with Trump ahead of the primary in her home state of South Carolina in late February.

Some analysts predicted that Haley's perceived momentum could stall out following a serious gaffe in which she failed to mention slavery when asked by a voter about the causes of the Civil War.

For months, both Haley and DeSantis have focused most of their energy on knocking each other out of the race with an eye on getting into a two-person race against Trump.

Even if Haley does elbow DeSantis aside, she would still face daunting odds of actually beating Trump. Polls of DeSantis supporters say Trump is their second choice, and they would likely line up behind the de facto leader of the GOP if the Florida governor abandons his race.