"Justice Scalia was an American hero," U.S. Sen. Ted Cruz tweeted. "We owe it to him, & the Nation, for the Senate to ensure that the next President names his replacement."
Florida U.S. Sen. Marco Rubio and retired neurosurgeon Ben Carson also said Scalia's successor should come from the next president, while Ohio Gov. John Kasich issued a statement mourning the loss but did not mention any potential nominee.
Donald Trump in a statement called Scalia "a remarkable person and a brilliant Supreme Court Justice, one of the best of all time."
Trump continued, “His career was defined by his reverence for the Constitution and his legacy of protecting Americans’ most cherished freedoms. He was a Justice who did not believe in legislating from the bench and he is a person whom I held in the highest regard and will always greatly respect his intelligence and conviction to uphold the Constitution of our country."
On the other side, Democratic front-runner Hillary Clinton called Scalia a "dedicated public servant who brought energy and passion to the bench."
But, Clinton said in a statement, Republicans who call for Scalia's seat to go unfilled until next year "dishonor our Constitution. The Senate has a constitutional responsibility here that it cannot abdicate for partisan political reasons."
Scalia's death will likely set off a testy and high-profile confirmation battle between Senate Republicans and Obama during his final year of office that could stretch for months. The Senate's schedule is thin this summer and autumn in anticipation of the November elections.
Senate Majority Leader Mitch McConnell, R-Ky., joined Cruz, Rubio and Carson in saying the seat should remain vacant until 2017. As the leader of the GOP caucus, McConnell has great power to make sure that happens.
Senate Republicans have already slowed the confirmation of Obama's other judicial nominations to a trickle. The slowdown can be attributed to the party's larger anger toward the president, as well as retaliation for a highly contentious rules change spearheaded in 2013 by then-Senate Majority Leader Harry Reid, D-Nev., which took away the GOP's power to filibuster most presidential nominations. The rules change, which the GOP has not reversed since taking power, does not impact Supreme Court nominations. That Obama will need to secure the support of 60 senators to install his nominee on the high court.
That rule change angered U.S. Sen. Lindsey Graham, R-S.C. Graham told reporters gathered here for tonight's Republican debate that that rule change means unless Obama nominates a consensus candidate, he will not get a nomination approved this year.
"If Hillary Clinton is elected president and she nominates a qualified liberal, I'll vote for him or her," Graham said.
Obama has gotten two justices nominees onto the Supreme Court bench: Sonia Sotomayor and Elena Kagan. One name that could pop up this time around is Leah Ward Sears, the former chief justice of Georgia's top court who was considered in 2009 for the spot that Sotomayor ultimately secured.
U.S. Rep. Mark Sanford, R-S.C., said the Senate should at least allow an Obama nominee to reach the floor.
"My sense would be yeah, but I'm not in the Senate," Sanford said. "I think it's part and parcel to the democratic process to hear anybody's perspective irregardless of whether you agree with him."
Supreme Court Chief Justice John G. Roberts, Jr., said Scalia was "an extraordinary individual and jurist, admired and treasured by his colleagues. His passing is a great loss to the Court and the country he so loyally served."
In Georgia, Republican U.S. Sen. Johnny Isakson called Scalia a patriot and agreed with McConnell that the Senate should wait to confirm another nominee.
“My personal feelings are we’re eight months away from an election in November and 10 months away from swearing in a new president of the United States. The American people are going to the polls to vote in November to pick the next president and I think the next president ought to be the one to fill that vacancy and not the president who’s going out," Isakson said in an interview Saturday night.
Isakson continued, “No risk of judgment when you’re talking about the Supreme Court is worth what it could do to the country by acting too fast at the wrong time."
Lithonia Democratic Rep. Hank Johnson said he had “tremendous confidence that President Obama will use the awesome power of his office to appoint a well-qualified replacement for Justice Scalia."
Johnson slammed Republicans for talk of holding up the nomination.
“It does tremendous damage to the legacy of a strict constructionist like Justice Scalia for senators or anybody else to suggest that politics be allowed to trump providence and that President Obama should hold off on nominating a replacement for Justice Scalia," he said in an interview.