As Republicans struggle to coalesce around a single rival to former President Donald J. Trump, the popular governors of Iowa and New Hampshire have also split their ticket.

Gov. Kim Reynolds of Iowa, which votes first in the Republican presidential nominating contest, is backing Gov. Ron DeSantis of Florida. Gov. Chris Sununu of New Hampshire, which votes second, is supporting Nikki Haley, the former United Nations ambassador and South Carolina governor.

On Tuesday, Mr. DeSantis played up the power of Ms. Reynolds’s backing while dismissing the potency of Mr. Sununu and calling Ms. Haley an avatar of “the old failed Republican establishment of yesteryear.”

“Even a campaigner as good as Chris is not going to be able to paper over Nikki being an establishment candidate,” Mr. DeSantis said during a town hall for Iowa voters broadcast by CNN on Tuesday, hours after Mr. Sununu announced his endorsement of Ms. Haley at an event in New Hampshire. “I mean, she’s getting funded by liberal Democrats from California like the founder of LinkedIn, people on Wall Street like the head of JPMorgan.”

For Mr. DeSantis, the town hall was a chance to make his pitch before a national audience without the name-calling and noisy cross-talk of the Republican presidential debates. He had entered the race as the clear favorite to upend Mr. Trump. But as frequent missteps have marred his campaign, some influential megadonors have thrown their support behind Ms. Haley, whom they see as more moderate.

Among them are the two donors name-checked by Mr. DeSantis, Reid Hoffman, the billionaire co-founder of LinkedIn, and Jamie Dimon, the chief executive of JPMorgan Chase. (Ms. Haley also has the backing of traditional Republican donors.)

Both Mr. DeSantis and Ms. Haley trail Mr. Trump by wide margins in polls nationally as well in the early-voting states. To close the gap, Mr. DeSantis has jumped at every opportunity to appear before Iowa voters, including the town hall hosted by CNN, a news organization that he has frequently derided as “corporate media.”

Many of the questions asked on Tuesday, both by the voters in attendance at Grand View University in Des Moines and the moderator, Jake Tapper, were less than hard-hitting, and Mr. DeSantis was able to have a largely easy and confident stage presence.

One voter asked him what food he most enjoyed at the Iowa State Fair. “Pork on a stick,” Mr. DeSantis replied with a smile, “but I did not do it in public because they said if they get a picture of it, you know, it’s a really bad thing.”

Mr. Tapper asked Mr. DeSantis, who often talks about “destroying leftism,” to name his favorite Florida Democrat. He responded with two county sheriffs in South Florida.

But Mr. DeSantis was also given the opportunity to detail some of his policy positions. On the Israeli-Palestinian conflict, Mr. DeSantis said he opposed a two-state solution. On Ukraine, he expressed support for efforts by Republicans in Congress to tie funding for its war against Russia to U.S. border security. On Social Security, he said seniors should keep their benefits and called for a bipartisan effort to ensure the program’s long-term stability.

“My grandmother lived till 91,” Mr. DeSantis explained. “Social Security was her sole source of income. So I understand what a lot of people are going through.”

Still, he was sometimes light on specifics.

Pressed by Mr. Tapper to say when he would release his plan to replace the Affordable Care Act, Mr. DeSantis said, “We’re working on it.”

He added: “You kind of campaign in poetry, then you govern in prose.”

And although he saved his harshest words for Ms. Haley, Mr. DeSantis also forcefully criticized Mr. Trump, something he has rarely done on national television.

In his first answer, Mr. DeSantis said that Mr. Trump had “dramatically” mishandled the economy during the coronavirus pandemic. He also said that Mr. Trump was “flip-flopping” on abortion by criticizing a six-week ban that Mr. DeSantis had signed in Florida. And he noted Mr. Trump’s failure to build a wall on the United States’ southern border and have Mexico pay for it, as he had pledged to do.

“It’s a different Donald Trump than ’15 and ’16,” he argued. “Back then he was colorful, but it was really America-first about the policies. Now, a lot of it’s about him.”

Mr. DeSantis has said that Mr. Trump must be beaten in Iowa if Republicans want to stop him elsewhere. He has devoted extensive resources to winning the state, visiting each of its 99 counties and moving roughly a third of his campaign staff there.

Outside groups are also helping his cause. One allied super PAC has built an extensive ground game to turn out support during the Jan. 15 caucuses. Another is investing heavily in advertisements targeting Ms. Haley.

And he has campaigned frequently with Ms. Reynolds, who endorsed him last month. In a radio interview on Tuesday before the town hall, Mr. DeSantis called her “a tremendous help.”

Other candidates are also focusing heavily on Iowa. The entrepreneur Vivek Ramaswamy plans to visit a total of 29 counties this week alone, according to his campaign. On Wednesday, Mr. Ramaswamy will appear in a similar CNN town hall in Des Moines.

But none of the efforts have seemed to move the polls. Mr. DeSantis now trails Mr. Trump by more than 30 points among Iowa Republicans, according to a Des Moines Register/NBC News/Mediacom survey released on Monday.

And in New Hampshire, where Mr. DeSantis has spent far less time, Ms. Haley has now pulled into second place. Mr. DeSantis has fallen to fourth or fifth.

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