Mainstream Republicans grappled on Sunday with Donald J. Trump's sweeping victory in South Carolina as if cycling through stages of grief, with some refusing to accept that he could be the party's eventual nominee and others searching for ways to prevent his insurgent candidacy from becoming unstoppable.
As his rivals headed west ahead of Tuesday's Nevada caucuses and "Super Tuesday" a week later, there was pressure on some of the party's most prominent figures to declare their support for Sen. Marco Rubio, who finished second in South Carolina — or at least to help rally people behind him as the most viable alternative to Trump.
Both Rubio and Sen. Ted Cruz of Texas, who finished third by a narrow margin, tried to make the case that the nominating fight was still at an early stage.
"Last night was truly the beginning of the real Republican primary," Rubio said on CNN.
Cruz continued to remind people that he had handed Trump his only defeat so far, in Iowa.
"If you want to beat Donald Trump, you've got to go with the only campaign that has demonstrated that they can beat Donald Trump," he said on ABC News.
Trump, who owns a hotel on the Las Vegas Strip, is widely seen as a favorite in the Nevada caucuses. From there, the race heads toward Super Tuesday on March 1, a patchwork of more than 10 states with 595 delegates at stake, where Trump's large rallies and ability to command free television time will aid him. A candidate needs 1,237 delegates to capture the nomination.
A pair of potential endorsements loom large in Rubio's hopes for vaulting ahead of Trump, who many Republicans fear could drag the party down with him in November. The critical endorsements are those of Mitt Romney, the 2012 presidential nominee, and Jeb Bush, the former Florida governor, who withdrew from the presidential race on Saturday.
Rubio's allies, who have been pushing for an endorsement from Romney, believe that his eventual backing is all but a certainty. But Romney, who strongly considered a 2016 presidential campaign of his own before bowing out as Bush made a show of fundraising force, is not yet ready to make an endorsement, according to three people close to him.
His advisers are also said to be split as to whether he should do so. But Romney has been incensed by the campaign that Trump has run, according to those close to him, though he has only occasionally spoken out publicly, as he did after Trump praised the Russian leader Vladimir V. Putin.
"Important distinction: thug Putin kills journalists and opponents," Romney wrote on Twitter. "Our presidents kill terrorists and enemy combatants."
Bush's backing will most likely be tougher to secure. He and Rubio clashed heatedly during the last few weeks of the campaign, and Bush was plainly wounded by the experience of being upstaged by his former political protégé.
In his remarks on the night of the South Carolina primary, Rubio praised Bush as a visionary governor and a good man. But it may take a more concerted effort at fence-mending to persuade Bush to join forces with Rubio against the two other major candidates in the race.
Another obstacle for Rubio is the presence of Gov. John Kasich of Ohio, who is fighting him for support from some of the same voters. Rubio's campaign openly made a push for Kasich to leave the race in a memo sent to reporters on Sunday.
"John Kasich has no path to the nomination," Rubio's advisers wrote, asserting that there was no way for Kasich to accrue the needed delegates.
Chris Schrimpf, a spokesman for Kasich, responded in kind.
"Rubio has consistently underperformed throughout this nominating process. He has the same number of second-place finishes as Gov. Kasich despite spending at least $45 million more," Schrimpf said. "His candidacy has not lived up to its promise despite all the hype. Rubio can't beat Trump in Florida, while we will beat him in Ohio."
Kasich, Cruz and Rubio each sought to recruit Bush's campaign donors. But not all Bush's financial supporters were immediately receptive to the idea of opening their wallets to a new presidential campaign.
Republicans aware of the conversations taking place among many of the party's biggest financiers on Sunday described a wariness from many Bush supporters who felt burned by having given so much to a losing cause. "It may take some time," said one of these people, who is now unaligned with a campaign.
Mica Mosbacher, a Cruz fundraiser based in Houston and New York, said she had begun placing calls to friends "who liked Cruz but stuck with Jeb out of family loyalty." She had resisted calling members of Bush's steering committee, she said, because "they need a moment of silence."
There was little evidence of either a partywide distress call or donors moving off the bench en masse toward Rubio, who has positioned himself to be the most palatable and electable remaining option for the Republican elites.
Fred Zeidman, a major Republican donor and longtime Bush family friend who backed Bush, said he planned to take a breath and see how things played out.
The same was true for Woody Johnson, owner of the New York Jets football team, who was Bush's national finance chairman. An aide to Johnson pointed out that he had invested a lot of time in helping Bush, even knocking on doors in early-voting states, and that he was not ready to shift allegiances so soon.
Johnson, long a friend of Trump's, has nonetheless found himself used as an object lesson over the last week by the Republican front-runner, who mentioned Johnson at rallies as an example of special-interest donors who supported candidates like Bush.
In a sign of how gingerly Trump's opponents continue to treat him, Rubio declined to attack him aggressively on Sunday. Asked about taking a more forceful approach, Rubio would say only that Trump's lack of foreign policy knowledge was worrisome.
Time is running short for Rubio to demonstrate that he can achieve a victory and thwart Trump: His home state of Florida will vote on March 15.
For his part, Trump was magnanimous in a round of television interviews Sunday. He argued that he was best suited to draw support from Democrats and independents in a general election against Hillary Clinton. And he went easy on his Republican opponents, even offering kind words about Bush, whom he had attacked viciously before.
"I wish him well — he's a nice person, he fought really hard," Trump said on MSNBC, adding that his son Eric was friendly with one of Bush's sons.
As soon as the polls closed in South Carolina on Saturday night, Rubio's supporters began firing off emails to Bush's backers, many of whom the Rubio supporters had remained in close contact with during the last few months in anticipation of Bush's campaign ending.
Some of Rubio's associates circulated data points from recent polls showing that he would defeat Trump if the Republican contest narrowed to a two-man race. Others were more blunt, arguing that their differences with Bush were never about him personally but instead rooted in their belief that Rubio was the only candidate with the broad appeal to win a general election.
"We'll see how it plays out," Rubio said Sunday as he was boarding a flight to Tennessee, which holds its primary as part of the Super Tuesday slate and is a place where Rubio hopes to pick up crucial delegates. "We feel like a lot of people that were on Jeb's team are people we're going welcome onto our team, people we've known for a long time."
But as the candidates projected confidence, members of the Republican establishment were filled with increasing anxiety about Trump's prospects.
Henry Barbour, a Republican National Committee member from Mississippi, sounded a note of alarm about Republicans continuing to wait to see how the race plays out.
"After Trump has won in New Hampshire and South Carolina, Republicans are crazy and about to blow the White House if we don't rally to stop him," Barbour said. "It's certainly time that we have to consolidate the race."
He predicted that Trump's nomination would not only cost Republicans the White House but also hurt the party's chances of keeping its majority in the Senate.
Some political strategists argued that too little had been done to take on Trump directly. Stuart Stevens, the top strategist to Romney in 2012, took issue with complaints that anti-Trump ads had failed to derail him. He pointed out that when Romney faced a challenge from Newt Gingrich, the former speaker of the House, it was a focused effort.
"No one is running a modern, focused, coordinated campaign against the front-runner as if they want to win," Stevens said.
Reporting was contributed by Ashley Parker, Jeremy W. Peters, Alexander Burns, Thomas Kaplan and Matt Flegenheimer.