By PATRICK HEALY and JONATHAN MARTIN

The Republican Party is facing a historic split over its fundamental principles and identity, as its once powerful establishment grapples with an eruption of class tensions, ethnic resentments and mistrust among working-class conservatives who are demanding a presidential nominee who represents their interests.

At family dinners and New Year’s parties, in conference calls and at private lunches, longtime Republicans are expressing a growing fear that the coming election could be shattering for the party, or reshape it in ways that leave it unrecognizable.

While warring party factions usually reconcile after brutal nomination fights, this race feels different, according to interviews with more than 50 Republican leaders, activists, donors and voters, from both elite circles and the grass roots.

Never have so many voters been attracted to Republican candidates like Donald J. Trump and Senator Ted Cruz of Texas, who are challenging core party beliefs on the economy and national security and new goals like winning over Hispanics through immigration reform.

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Rank-and-file conservatives, after decades of deferring to party elites, are trying to stage what is effectively a people’s coup by selecting a standard-bearer who is not the preferred candidate of wealthy donors and elected officials.

And many of those traditional power brokers, in turn, are deeply uncomfortable and even hostile to Mr. Trump and Mr. Cruz: Between them, the leading candidates do not have the backing of a single senator or governor.

“I haven’t seen this large of a division in my career,” said Senator John McCain, the Arizona Republican first elected to Congress in 1982. “You probably have to go back to Ford versus Reagan in 1976. But that was only two people.”

The issues animating grass-roots voters — opposition to immigration, worries about wages and discomfort with America’s fast-changing demographics — are diverging from and at times colliding with the Republican establishment’s interests in free trade, lower taxes, less regulation and openness to immigration.

The fractures could help a Democrat win the White House if Republicans do not ultimately find ways to unite, as one candidate, Gov. Chris Christie of New Jersey, warned last week.

The divide was evident at a recent Greenville, S.C., gathering of bankers and lawyers, reliable Republicans who shared tea and pastries and their growing anxieties about where their party is going. In a meeting room near the wooded shore of Furman Lake, the group of mostly older white men expressed concern that their party was fracturing over free trade, immigration and Wall Street. And they worried that their candidates — mainstream conservatives like Jeb Bush — were losing.

“It’s all really hard to believe that decades of Republican ideas are at risk,” said Barry Wynn, a prominent Bush donor at the meeting.

The strains on Republicanism are driven home by scenes like the 1,500 people who waited two hours in 10-degree weather on Tuesday night to see Mr. Trump campaign in Claremont, N.H. And the 700 who jammed the student center of an Iowa Christian college the same evening to hear Mr. Cruz. These crowds were full of lunch-bucket conservatives who expressed frustration with the Republican gentry.

“The Republican Party has never done anything for the working man like me, even though we’ve voted Republican for years,” said Leo Martin, a 62-year-old machinist from Newport, N.H., who attended Mr. Trump’s Claremont rally. “This election is the first in my life where we can change what it means to be a Republican.”

This anger has transformed the quadrennial exercise of picking a Republican nominee into a referendum on the future of one of the country’s two enduring political parties. Patrick J. Buchanan, a Nixon and Reagan adviser who ran for the Republican nomination in 1992 and 1996 by stressing the economic and cultural concerns of working-class Americans, said these voters were roiling the party because they had “suffered long enough.”

Mr. Buchanan cited years of job losses and wage stagnation that he blamed on free-trade deals and cheap labor from illegal immigrants, as well as hardships from foreign wars that have hit families whose children enlisted in hopes of better lives.

“The chickens have come home to roost,” Mr. Buchanan said. “Putting the party back together again will be very hard after this nomination race. I think the party is going to shift against trade and interventionism, and become more nationalist and tribal and more about protecting the border.”

Anger and alienation have been simmering in Republican ranks since the end of the George W. Bush administration, at first over policy and then more acutely over how the party should respond to the country’s changing demography.

“All the things the voters want have been shoved off to sidelines by Republican leaders,” said Laura Ingraham, a talk-show host who was a force behind the primary election defeat of Eric Cantor, then the House majority leader, in 2014. “And the voters finally have a couple of people here who are saying this table has to be turned over.”

The splits within the party would be difficult to heal no matter the nominee. If an establishment candidate wins the nomination, the highly energized voters backing Mr. Trump and Mr. Cruz may revolt; about two-thirds of Trump supporters would vote for him as a third-party candidate, according to a Suffolk University/USA Today poll last month — a possibility that could help the Democratic nominee. If Mr. Cruz is nominated, he will have to win over party leaders while not appearing to be selling out to his anti-establishment supporters. A Fox News poll released on Friday found that 66 percent of Cruz supporters in Iowa felt “betrayed” by politicians in their party.

If party leaders backed Mr. Trump, they would have to conduct campaigns in parallel universes, supporting a candidate who has said he wants to deport illegal immigrants en masse and temporarily bar Muslims from the country, while simultaneously trying to diversify their predominantly white male base.

Republican congressional leaders last week asked Gov. Nikki R. Haley of South Carolina, the daughter of Indian immigrants, to deliver the party’s response to the State of the Union speech this week, and invited King Abdullah II of Jordan, perhaps America’s closest ally in the Arab world, to address a joint session of Congress.

“I know Republicans who will support Hillary if Trump or Cruz is the nominee, no question,” Dick Thornburgh, an attorney general under President George Bush and a former Pennsylvania governor, said of Hillary Clinton. “Trump, especially, would split the party. But many will fall in line, seeing no choice.”

Mr. McCain, the 2008 Republican presidential nominee, and Mr. Graham, who was a presidential candidate until last month, said they would honor the will of the voters and support any eventual nominee. But Mr. Graham said the severity and impact of the party split would ultimately depend on whether a Republican won the presidency.

“If Trump or Cruz wins the White House, then my side of the party has to re-evaluate who we are, what we stand for, and I’d be willing to do that,” Mr. Graham said. “But if Trump or Cruz loses the presidency, would their supporters re-evaluate their views on immigration and other issues that would grow the party? If they do that, we can come back together. If they don’t, the party probably splits in a permanent way.”

Other Republicans said they believed that Mr. Cruz, if he won the nomination, would be similar to the archconservative Barry Goldwater, who was nominated in 1964, and that the party would survive the experience.

The presidential historian Richard Norton Smith, who has written biographies of some of the 20th century’s leading Republicans, said a nomination of Mr. Trump would represent “a hostile takeover” of the party, and make it more difficult for old-guard party leaders to suppress the passions of a more hard-core, anti-immigration, angry base.

“The nativists aren’t going away,” Mr. Smith said. “They might, if anything, become more feverish.”

Some political leaders, eyeing the Republican split, are sensing opportunity.

Michael R. Bloomberg, the billionaire media executive and former New York mayor, was intrigued enough by the prospect of Mr. Trump’s becoming the Republican standard-bearer that he commissioned a poll last month testing how he would fare against Mr. Trump and Mrs. Clinton, according to two sources close to Mr. Bloomberg. But he has often very publicly flirted with a run, savored the attention, then announced that he would not pursue the candidacy.

Whatever Mr. Bloomberg decides, the election so far has been upended by voters who live far from his world and, for the first time in years, feel as if their voices are being heard. Dave Conger, 60, a salesman who showed up at a Cruz campaign stop last week with a Cruz pin on his chest, said he had worked to elect both President George W. Bush and his father, but “was told a lot of things and nothing ever happened.”

He added, “This time I’m actually hearing somebody who’s telling me the truth; they’re actually going to go in and do something they say they’re going to do.”