Senators Marco Rubio and Ted Cruz, fighting for their political lives, relentlessly demeaned and baited Donald J. Trump at Thursday's debate, all but pleading with Republicans to abandon a candidate with a long history of business failures, deep ties to the Democratic Party and a taste for personal insults.
Warning that Mr. Trump would lead the party to a historic defeat in November, Mr. Rubio and Mr. Cruz delivered their attacks with urgency, as if trying to awaken voters who had fallen under Mr. Trump's spell. Mr. Rubio derided Mr. Trump as untrustworthy and uncivil, while Mr. Cruz bashed him for donating money to Hillary Clinton's 2008 presidential campaign and to other Democrats. Mr. Trump looked on with disgust, but as in their 10 previous debates, he seemed impervious and perhaps unstoppable.
At times, the face-off in Detroit also deteriorated into the kind of junior high school taunts that have startled many Republican elders but have done little to dent Mr. Trump's broad appeal. As Mr. Trump and Mr. Rubio traded insults over their manhood, Mr. Trump recalled Mr. Rubio's innuendo that Mr. Trump's "small hands" correlated with another part of his anatomy.
Mr. Trump, who has boasted about his sexual exploits, insisted that nothing was small about him. "I guarantee you," he continued with little subtlety, "there's no problem. I guarantee you."
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The two senators repeatedly urged Republicans to align against Mr. Trump in nominating contests over the next two weeks, saying that Mr. Trump could sew up the nomination even though a majority of voters so far have cast ballots for other candidates.
"Two-thirds of the people who cast a vote in a Republican primary or caucus have voted against you," Mr. Rubio told Mr. Trump. "The reason why is because we are not going to turn over the conservative movement or the party of Lincoln or Reagan, for example, to someone whose positions are not conservative."
The pleas reflected not only Mr. Trump's advantage in the race, but also the party's growing disquiet about the implications of nominating him. The specter of Mr. Trump as the Republican standard-bearer has long troubled both establishment-aligned and conservative leaders. But his initial hesitation to condemn the Ku Klux Klan in an interview on Sunday, and his success in seven states on Super Tuesday, have set off a new wave of anxiety that Mr. Trump could tarnish the party this year and perhaps beyond.
Still, in a striking moment, all of Mr. Trump's rivals on stage indicated that they would support him if he became the Republican nominee. The consensus was especially unusual in the case of Mr. Rubio, who has been caustically attacking Mr. Trump as a "con man."
While Mr. Rubio savaged Mr. Trump repeatedly on Thursday, Mr. Cruz combined his jabs with high-minded appeals to conservatives. He emphasized his support for a "simple flat tax" and a strong national defense, trying to position himself ahead of Mr. Rubio as the more competitive candidate against Mr. Trump.
Mr. Cruz also appealed directly to Mr. Trump's supporters by saying that their desire for a political outsider to lead the country was misplaced.
"For 40 years, Donald has been part of the corruption in Washington that you're angry about," Mr. Cruz said. "And you're not going to stop the corruption in Washington by supporting someone who has supported liberal Democrats for four decades, from Jimmy Carter to John Kerry to Hillary Clinton."
"Donald Trump in 2008 wrote four checks to elect Hillary Clinton as president," Mr. Cruz added, turning to Mr. Trump to demand why he had done so.
"Actually, it was for business," Mr. Trump said, before noting that he had also given to Ronald Reagan and George W. Bush.
Mr. Trump found himself on the defensive throughout the night, challenged by his rivals and the Fox News moderators to explain his inconsistent stands in the past. He also had to defend himself against a movement begun earlier Thursday by Mitt Romney, the 2012 Republican nominee, who shredded Mr. Trump as a "phony" and a "fraud" who must be blocked from the nomination.
Mr. Trump, offered the chance to respond to Mr. Romney with harshness or with substance, chose the former.
"He was a failed candidate," Mr. Trump said. "He should have beaten President Obama very easy."
Mr. Cruz and Mr. Rubio, who have been grappling for ways to halt Mr. Trump's political momentum, seemed intent on trying to bait him into losing his cool. At one point, as Mr. Cruz tarred Mr. Trump for donating to Mrs. Clinton's 2008 campaign, Mr. Trump tried repeatedly to interrupt.
"Count to 10, Donald — count to 10," Mr. Cruz said. Later, in an exchange over Supreme Court nominations, Mr. Cruz taunted, "Breathe, breathe, breathe — you can do it." That prompted Mr. Rubio to joke that his two rivals were primed for yoga, especially Mr. Trump. "He's very flexible," Mr. Rubio said, a quip referring to Mr. Trump's changes in political positions.
Mr. Rubio tried to get under Mr. Trump's skin by boring in on Trump University, the defunct education and training venture over which Mr. Trump is facing civil litigation alleging that he defrauded students. Recalling that he had spoken to "one of the victims," Mr. Rubio said that what students had gotten in the courses was "stuff you could pull off of Zillow."
"Why won't you give them their money back?" Mr. Rubio asked.
Mr. Trump, who described the litigation as "a minor civil case," claimed that almost all students who had signed up for the courses "said it was terrific," but he quickly lost patience with Mr. Rubio. Calling him "little Marco" — a phrase he used several times — Mr. Trump noted that the senator was losing to him in Florida polls before the state's March 15 primary.
"The people in Florida wouldn't elect him dogcatcher," Mr. Trump said.
Mr. Rubio, his voice ragged, appeared frustrated at times as he repeatedly sought to sow doubts about Mr. Trump. He has been trying for months to catch fire against Mr. Trump, whom he holds in low regard on policy matters, and now the Florida primary looms as make-or-break for Mr. Rubio's candidacy.
"You have yet to answer a single serious question about any of this," Mr. Rubio said, referring to Mr. Trump's generalities on foreign affairs. As Mr. Trump responded by reiterating praise he had received from President Vladimir V. Putin of Russia, Mr. Rubio threw his arms up and turned away in exasperation.
If Mr. Trump struggled to deflect the attacks on his character, business sense and political viability against Mrs. Clinton in the fall, he seized opportunities to reassure conservatives that he would be a forceful commander in chief. Questioned by the moderators about his past advocacy for torture and for killing the families of terrorists, Mr. Trump stood firm and argued that "we should go tougher than waterboarding." Pressed about whether military officers would carry out such orders — killing terrorists' family members would violate the Geneva Conventions — Mr. Trump offered a boast.
"If I say 'do it,' they're going to do it," he said.
At another point, in a rare concession from Mr. Trump, he acknowledged that he was "changing" one of his positions in the highly charged immigration debate and was now open to offering visas for highly skilled foreign workers. He also lamented that foreign citizens "go to the best colleges" in America and "as soon as they are finished, they get shoved out," and said he was "softening the position because we have to have talented people in this country."
While his shift could appeal to some business leaders and moderate voters he would need in a general election, his campaign also issued a statement after the debate saying he would "institute an absolute requirement to hire American workers first for every visa and immigration program. No exception."
Mr. Trump's shifting positions have been a target for months, but during this debate, his rivals received help from the Fox News debate moderators. They played a compilation of video clips in which he was depicted changing his mind on issues like the war in Iraq. Mr. Trump was then asked directly if he had "a core."
"I have a very strong core, but I have never seen a successful person who wasn't flexible," Mr. Trump said.
One of the most anticipated face-offs of the night was between Mr. Trump and the moderator Megyn Kelly, who infuriated the candidate with her aggressive questions at the first Republican debate in August. Ms. Kelly and Mr. Trump breezily engaged each other on Thursday night, but Ms. Kelly was pointed if polite in her questioning.
Both Mr. Rubio and Mr. Cruz repeatedly challenged Mr. Trump to release the full transcript of his meeting with The New York Times's editorial board earlier in the year. BuzzFeed reported this week that Mr. Trump, in off-the-record comments, had told the newspaper that he was willing to soften his hard-line immigration views.
But Mr. Trump stood his ground, saying he would "never release off-the-record conversations." Pressed by Mr. Cruz, he shot back: "I've given my answer, lying Ted. I've given my answer."
The fourth candidate, Gov. John Kasich of Ohio, who has positioned himself as the positive-sounding and seasoned executive in the race, largely stuck to that strategy. But Mr. Kasich, who is lagging far behind Mr. Trump and the other candidates, struggled to leave a mark in the debate.