Easley, S.C. -- The day after a strong performance in the latest Republican presidential debate, Florida U.S. Sen. Marco Rubio told more than 2,000 supporters that the death of Supreme Court Justice Antonin Scalia has permanently changed the race for the White House.

Rubio, speaking at Easley High School, praised Scalia, who passed Saturday at the age of 79.

"We commend his soul to God, we pray for his family and now we pray for the country," Rubio said. "Because that vacancy has to be filled. And it will be filled by the next president. Not by this one."

There is no way, Rubio said, the Senate should confirm anybody President Barack Obama tries to appoint in his final year in office.

Earlier Sunday on NBC's "Meet the Press," Rubio deflected questions from host Chuck Todd about whether it was the Senate's obligation to vote on Obama's nominee.

"We will go through the motions but not while Barack Obama is in White House," Rubio said.

Rubio also said there is precedent for the president not to nominate, and the Senate not to act, on Supreme Court justices in an election year.

"You stop the advise and consent process," Rubio said.

The bottom line, he said, is "the balance of the court is at stake. We’re not moving forward on it."

It's something on which Rubio and U.S. Sen. Ted Cruz agree. Cruz likewise told Todd "there is a long tradition you don’t do this in an election year. We ought to make the 2016 election a referendum on the Supreme Court."

But U.S. Sen. Elizabeth Warren, D-Mass., in a statement on Facebook, slammed Republicans, including Senate Majority Leader Mitch McConnell, R-Kentucky, for their immediate refusal to consider a vote.

Said Warren: