Republican White House hopefuls have called for US president Barack Obama to step aside and allow his successor to nominate the next Supreme Court justice, following the death of ultra-conservative judge Antonin Scalia.
Only Jeb Bush said Mr Obama had "every right" to nominate a justice during his final year in office.
The former Florida governor said there should be “consensus orientation on that nomination”, but added that he did not expect Mr Obama would pick a candidate in that vein.
The five other candidates on the stage in the debate in Greenville, South Carolina, urged the Republican-led Senate to block any attempts by the president to get his third nominee on the court.
"It's up to (Senate majority leader) Mitch McConnell and everybody else to stop it," billionaire businessman Donald Trump said. "It's called delay, delay, delay."
Donald Trump and Jeb Bush clashed angrily over the Iraq war, the Bush family and Mr Trump's business dealings.
With the Republican candidates increasingly anxious for a good showing in the first primary in the American south on February 20th, fights between Mr Trump and Mr Bush dominated the two-hour debate hosted by CBS.
Ahead in the polls, Mr Trump came under sustained fire from his rivals and there also were plenty of finger-pointing exchanges between Mr Trump and Texas Senator Ted Cruz.
Mr Cruz and Florida Senator Marco Rubio, competing with Mr Bush to emerge as the main anti-Trump alternative, battled over illegal immigration.
Mr Trump, leading polls in South Carolina and in position to take command of the Republican nomination fight if he wins the state, attacked Mr Bush's brother, former President George W Bush, for launching the Iraq war in 2003. "A big, fat mistake," Mr Trump said.
It was the most bitter exchange between them over the course of nine debates ahead of the November 8th presidential election and was a sign of how critical both see a strong showing in South Carolina.
"George Bush made a mistake," Mr Trump thundered. "We all make mistakes. But that one was a beauty ... They lied! They said there were weapons of mass destruction. And there were none."
Many in the crowd booed Mr Trump and the Republican front-runner dismissed them as "lobbyists and special interests" who supported Jeb Bush, the former Florida governor.
Mr Bush also criticised Mr Trump for remarks praising Russian president Vladimir Putin, saying Mr Putin is stirring turmoil in Syria by launching air strikes in support of Syrian president Bashir Assad, who Washington would like to leave power.
Mr Bush, who will campaign on Monday with his brother George, rejected Mr Trump's comments and defended his family.
"I'm sick and tired of him going after my family," Mr Bush said. "My dad is the greatest man alive in my mind. While Donald Trump was building a reality TV show, my brother was building a security apparatus to keep us safe. And I'm proud of what he did.
"He had the gall to go after my mother," Mr Bush said, reminding the audience that Mr Trump had criticised his 90-year-old mother, Barbara Bush, wife of former president George W Bush. "My mother is the strongest woman I know."
"She should be running," Mr Trump responded.
Mr Bush provoked another outburst from Mr Trump by saying the Republican nominee should be someone "who doesn't brag, for example, that he has been bankrupt four times."
"That's another lie," said Mr Trump. "I never went bankrupt."
Trump Vs Cruz
Mr Trump also had a heated exchange with Mr Cruz when the senator said Mr Trump would appoint liberals to the supreme court.
"You are the biggest liar," Mr Trump said sharply.
As they tried to talk over each other, Mr Cruz chided Mr Trump by saying, "Adults don't interrupt."
Ohio Governor John Kasich, who finished second in the New Hampshire primary last Tuesday and who pushes an optimistic message, called for calm.
"These attacks, some of them are personal. I think we're fixing to lose the election to (Democratic front-runner) Hillary Clinton, " he said.
Mr Trump's attacks on the Bush family carried risks for him, since many US military veterans in South Carolina have long supported the family.
Mr Cruz and Mr Rubio renewed their battle over who is the toughest on illegal immigration with Mr Cruz insisting that Mr Rubio, as part of a Gang of Eight senators who sought a compromise on legislation in 2013, was for "amnesty" but now is against it for political purposes.
He insisted that Mr Rubio had said in Spanish on Univision that he would not rescind an executive order signed by president Barack Obama in support of the children of illegal immigrants.
Mr Rubio shot back: "I don't know how he knows what I said on Univision because he doesn't speaking Spanish."
As the crowd roared, Mr Rubio said Mr Cruz is "telling lies... He's lying about all sorts of things and now he makes things up."
The Bush campaign laid into Mr Trump for criticising his family. "I'm sick and tired of Trump attacking my family. This isn't about my family or his family. It's about your family. #GOPDebate," Bush's official account (@JebBush) tweeted during the debate.
The hashtag #GOPDebate was the top-trending item on Twitter Saturday night.
Mr Trump dominated the bulk of the conversation in the first half, with 42 per cent of the mentions associated with the hashtag #GOPDebate, according to Twitter data. Mr Bush was a distant second, with 23 per cent of the conversation.