Scalia's sudden death rocked Washington the 2016 presidential campaign. Senate Majority Leader Mitch McConnell, R-Ky., immediately announced his intent to block a vote on any replacement for Scalia nominated this year by President Obama.
"This vacancy should not be filled until we have a new president," McConnell said in a statement.
McConnell's move received the endorsement from Republican presidential candidates.
"Delay, delay, delay," Donald Trump urged Senate Republicans during a GOP debate Saturday night.
In an address Saturday night to the country, Obama mourned Scalia's death, but made it clear he will nominate a new justice, setting up a what looks likely to be an almost unprecedented fight over a Supreme Court vacancy in an election year.
"I plan to fulfill my Constitutional responsibilities to nominate a successor in due time," he said.
"These are responsibilities that I take seriously as should everyone," Obama said. "They are bigger than any one party."
McConnell can probably succeed in blocking action on a new nominee. But Democrats hope doing so will cost the GOP in the presidential and congressional elections, by leaving the GOP open to charges of obstructing the prescribed constitutional process for partisan advantage.
GOP candidates brawl in South Carolina Debate:
The six remaining Republican presidential candidates took the stage in Greenville, S.C., just hours after news of Scalia's death.
Honoring Scalia's colorful argumentative style, if not his wit, the candidates brawled in perhaps their most pointed debate so far.
Florida Sen. Marco Rubio and Donald Trump both called Texas Sen. Ted Cruz a liar, accusing Cruz of distorting their records. Former Florida Gov. Jeb Bush and Ohio Gov. John Kasich argued over Kasich's expansion of Medicaid in his state.
But the most pitched exchange came between Trump and Bush over the somewhat unlikely topic of September 11, 2001 terror attack and the ensuring invasion of Iraq.
Trump reacted loudly to Bush's claim that this brother, former President George W. Bush, "kept us safe" after the attack, a claim that amounts to a defense of the Iraq War. Sounding like a 2005 Democrat, which rivals charge he was, Trump said the Bush administration lied to justify the invasion.
"They said there were weapons of mass destruction, there were none," Trump said. "And they knew there were none."
Trump said the former president, who is set to campaign for his brother in South Carolina this week, bears responsibility for failing to stop the 9/11 attack.
"The World Trade Center came down during your brother's reign, remember that," Trump said. "That's not keeping us safe."
Trump has departed from conservative orthodoxy on many issues: health care, the value of Planned Parenthood, eminent domain, Social Security and free trade. But his angry assertion of what many outside the GOP consider settled conclusions on Iraq may be his riskiest departure.
George W. Bush retains popularity among conservative primary voters in South Carolina and other primary states. Trump, who polls show holding a huge lead in South Carolina, may not be catchable there with a week until the primary, but many political analysts wondered if Iraq will prove the issue on which Trump loses GOP voters.
Amid triumphant tweets touting what he claimed was "my best performance yet," at a debate, Trump also showed signs of concern. The real estate developer seemed to walk back his statements on Iraq and 9/11 during an appearance Sunday morning on CBS' "Face the Nation."
"I am not blaming him," Trump said, when asked about his statements on George Bush's failure to avert the 9/11 attack.
Trump also watered down his statement claim that Bush administration officials lied about Iraq. President Bush "thought there were weapons of mass destruction, maybe, or maybe he didn't," Trump said.
Elsewhere Sunday, Sen. Bernie Sanders of Vermont, continued to court African American voters whose support he will need in South Carolina and elsewhere to compete with Hillary Clinton for the Democratic nomination. Sanders appeared in a taped interview Sunday with Rev. Al Sharpton.
Tough talk on Russia as Syrian ceasefire talks flounder:
Speaking at a security conference in Munich, Prime Minister Dmitry Medvedev said Russia and western states have entered "a new Cold War." His complaint comes after confrontation over Russia's annexation of Crimea and efforts to destabilize Ukraine and amid recent tension over Russia's military support for Syrian President Bashar Assad.
President Obama called Russian President Vladimir Putin Saturday, according to the White House, to "stress the importance of rapidly implementing humanitarian access to besieged areas of Syria and initiating a nationwide cessation of hostilities."
The statement said Obama "emphasized the importance now of Russia playing a constructive role by ceasing its air campaign against moderate opposition forces in Syria."
But in an address at the same security conference in Munich on Sunday, Sen. John McCain, R-Ariz., the chairman of the Senate Armed Services Committee, blasted Obama's diplomacy with Putin and well as Iran, as naive and weak.
"Mr. Putin is not interested in being our partner," McCain said.
"He wants to exacerbate the refugee crisis and use it as a weapon to divide the Transatlantic alliance and undermine the European project," McCain charged.
McCain said deals with Syria and Iran, along with failure to confront Russia, could convince allies that the United States is "untrustworthy and feckless."