WASHINGTON -- Sounding like he is prepared for a lengthy vacancy on the Supreme Court bench, Justice Samuel Alito said Tuesday that the court will find a way to get its work done with eight members following the death of Antonin Scalia.

"We will deal with it," Alito told a Georgetown University law school audience Tuesday after he was asked a question about Senate Republicans' resolve to oppose anyone President Barack Obama nominates to take Scalia's place.

The court has functioned with an even number of justices before, Alito said, noting that the Constitution does not set the court's size. The court initially was made up of six justices, before it eventually grew to nine. During the Civil War, Congress added a 10th seat.

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"They must have been more agreeable," Alito joked.

The court was back in session Monday for the first time since Scalia's death, CBS News correspondent Jan Crawford reported. With Scalia's seat on the bench draped with a black cloth, Chief Justice John Roberts started the morning session with a tribute: "We remember his incisive intellect, his agile wit, and his captivating prose. But we cannot forget his irrepressible spirit."

The court is almost certain to be without a new justice through at least late June, when the court usually issues its final decisions for the term. The justices could divide 4-4 in some of the term's big cases involving abortion, labor unions and immigration. A tie vote would leave the lower court ruling in place and prevent the Supreme Court from resolving the issues for the whole country.

Alito sidestepped a question about what kind of person should take Scalia's place, saying the president and the Senate will make that call. "I have enough trouble with the questions I have to decide," he said.

The bench of late Supreme Court Justice Antonin Scalia is seen draped with black wool crepe in memoriam inside the Supreme Court in Washington in this February 16, 2016 file photo. REUTERS

Meantime, Republicans on the Senate Judiciary Committee on Tuesday ruled out any hearing for President Obama's nominee to the Supreme Court, insisting that the choice rests with the president's successor.

"Because our decision is based on constitutional principle and born of a necessity to protect the will of the American people, this committee will not hold hearings on any Supreme Court nominee until after our next president is sworn in on January 20, 2017," they said in a letter to Majority Leader Mitch McConnell.

"I agree with the Judiciary Committee's recommendation to not have hearings. In short, there will not be action taken," McConnell told reporters.

Even the most divisive nominees for the high court have received a hearing before the Judiciary Committee, and the election-year decision to deny such a session is a sharp break with the Senate's traditional "advise and consent" role. A committee review and a hearing is the first step in the process.

Scalia's Feb. 13 death ignited a major fight in Washington over whether Obama should be able to replace him in a presidential election year. He had been dead only for a few hours when McConnell announced that he would oppose replacing him before the election.

The Republicans' action is certain to have repercussions, not only in the presidential race but in congressional contests where vulnerable Senate incumbents in Illinois, Wisconsin, Ohio, Pennsylvania and New Hampshire face tough Democratic challengers. At least one of those senators, Republican Mark Kirk of Illinois, has suggested holding hearings.

But Republican members of the committee met with McConnell and emerged with a simple message: "No hearing, no vote," said Sen. Lindsey Graham.

Confirmation hearings for a Supreme Court nominee are the most high-profile in the Senate, and any session is certain to be a spectacle. Among the members of the panel is Republican presidential candidate Ted Cruz, and the Texas senator has vowed to block any nominee.

White House spokesman Josh Earnest said it was "absolutely" still possible the Senate would hold hearings, pointing to a handful of Republicans who he said had expressed a willingness, including Kirk, Susan Collins of Maine, Dan Coats of Indiana and Roy Blunt of Missouri.

Earnest said in the last day, Obama has spoken to Republican lawmakers, including some on the committee.

Republicans pointed to a 1992 speech by Vice President Joe Biden, then the chairman of the Judiciary Committee, in which he said that in a presidential election year the Senate should "not consider holding hearings until after the election." As it turned out, there was no opening on the court that year.