All eyes will be on New Hampshire's undeclared, or independent, voters next week for the first-in-the-nation presidential primaries following reports of cross-party voting by Democrats in support of former U.N. Ambassador Nikki Haley during Monday's Iowa caucuses. 

Although former President Donald Trump achieved a historic victory in the Hawkeye State with more than 50% of the vote, well ahead of Haley's third-place finish, it wasn't for lack of trying by Democrats and independents opposed to the former president. They reportedly showed up at some caucus sites and caused a shortage of party registration forms. 

Even though registered Republicans were the only voters allowed to vote in Iowa's caucuses, the state allows same-day party registration, meaning Democrats and independents could show up, register and vote all in one evening.

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Former U.N. Ambassador Nikki Haley

Nikki Haley, former ambassador to the United Nations and 2024 Republican presidential candidate, during a campaign event in Bretton Woods, N.H., Tuesday, Jan. 16, 2024. (Adam Glanzman/Bloomberg via Getty Images)

At one caucus site in Johnson County, the only county Trump lost to Haley, by a single vote, caucus workers had to scramble for more printer paper to have enough forms to accommodate those trying to switch their party registration to Republican, according to CBS News.

Other reports also pointed to meddling by Democrats, including one voter who told Axios that switching party registration for a day was "a chance to diminish Trump's inevitability." Another said, "I believe all Americans should cast a vote against Donald Trump every chance we have."

By contrast, David Barker, the treasurer of the Iowa Republican Party, told Fox News Digital that although there were some new registrations for the party from Democrats and independents, a vast majority of those registering on the night of the caucus were first-time voters ready to oust President Biden.

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Despite any such effort to oppose Trump, it wasn't enough to boost Haley ahead of her main challenger for second place, Florida Gov. Ron DeSantis, who bested her by around 2,300 votes.

DeSantis in New Hampshire

Republican Florida Gov. Ron DeSantis at a campaign stop in Hampton, N.H., Wednesday, Jan. 17, 2024. (Paul Steinhauser/Fox News)

Looking ahead to next week's New Hampshire primary, approximately 3,500 Democrats in the state switched their party registration to become undeclared voters, or independents, ahead of the October deadline. Part of that effort was led by former New Jersey Gov. Chris Christie, who recently dropped out of the race, encouraging voters to take every opportunity to turn out against Trump.

Undeclared voters in New Hampshire, who make up a plurality of the Granite State's electorate, can choose whether to vote in the Democratic or Republican primary, and have long played a crucial role in determining who will be the non-incumbent party's nominee for president. The state does not allow intra-party voting.

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Some argue New Hampshire's undeclared voters who show up to vote on Tuesday will likely cast a ballot in the Republican primary considering President Biden isn't facing any serious challenge to his likely nomination for the Democrats. As one New Hampshire voter put it, the GOP race is "where all the action is."

Others, such as Dante Scala, a political science professor and researcher at the University of New Hampshire, say whether anti-Trump independents show up to vote for Haley "depends on their perception of Trump's inevitability."

Former President Donald Trump New Hampshire

Former President Donald Trump, a Republican presidential candidate, points to supporters at the conclusion of a campaign rally at the Atkinson Country Club Jan. 16, 2024, in Atkinson, N.H. (Brandon Bell/Getty Images)

"I think some of those voters would like to stick it to Trump if they could, but they really liked Chris Christie because he was purely anti-Trump. Haley is not. The question always is, will they show up? And I think they need a clear reason to do so. … If they're looking at the polling in New Hampshire, and they're listening to reports, and the vibe is 'Trump's got it in the bag,' then I think there will be less interest in showing up," Scala said. 

"If you're a Democratic leaner, you're not crazy about going to vote in a Republican primary in the first place. That kind of cuts against the grain. Haley's a pretty mainstream Republican, and so you're really uncomfortable with that. So, you would kind of need a good reason to do it."

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Haley campaign spokeswoman Olivia Perez-Cubas told Fox News Digital the ambassador has "always believed that the Republican Party has to be about addition, not subtraction." 

"Otherwise, Republicans will keep losing like we did in 2018, 2020 and 2022. If Republicans want to start winning again, we have to start bringing in voters who are fed up with Joe Biden, not pushing them away," she said.

Haley signs New Hampshire

Campaign signs for Nikki Haley, former ambassador to the United Nations and 2024 Republican presidential candidate, prior to a campaign event in Bretton Woods, N.H., Jan. 16, 2024. (Adam Glanzman/Bloomberg via Getty Images)

A senior Trump campaign official told Fox News Digital the "only people" voting for Haley are Democrats trying to interfere in the Republican primary because she "is a desperate globalist who wants higher taxes, open borders and China to dominate the United States."

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Fox News Digital also reached out to the DeSantis campaign for comment.

According to a new poll released Wednesday by Suffolk University, the Boston Globe and NBC10 in Boston, Trump remains the clear frontrunner over Haley in New Hampshire with 50% support to her 34%. DeSantis stands at 5% and is expected to head to South Carolina, Haley's home state, this weekend to start campaigning there.

Get the latest updates from the 2024 campaign trail, exclusive interviews and more at our Fox News Digital election hub.