Republican leaders on the U.S. Senate Judiciary Committee said Tuesday they wouldn’t hold hearings on a nominee from President Barack Obama. The move could result in the president not being able to immediately fill the U.S. Supreme Court seat vacated by the death of Justice Antonin Scalia earlier this month, the Washington Post reported.

After Scalia's death, Republican leaders have kept a common refrain: that the next president should be the one to pick the next justice. Republicans exiting a meeting with Senate Majority Leader Mitch McConnell, R-Ky., said there was a consensus view on the panel that they wouldn’t hold hearings on an Obama nominee.

McConnell didn’t elaborate on any ideas the committee might have but is expected to address the issue later Tuesday. A lunch was being held Tuesday with the conference of Senate Republicans, where nonjudiciary leaders within the GOP will also provide input on looking at an Obama Supreme Court nominee.

“We believe the American people need to decide who is going to make this appointment, rather than a lame-duck president,” Senate Majority Whip John Cornyn, R-Texas, told CNN.

Democrats have aligned themselves with Obama, arguing that he has more than 300 days left in the White House, and it would be detrimental to not have a ninth member of the Supreme Court for that long, NBC News reported. Only two Senate Republicans so far have said they want to have hearings on an Obama nominee — Susan Collins of Maine and Mark Kirk of Illinois, neither of whom are on the Judiciary committee.

“There’s still 11 months left in the president’s term here, which provides ample time for the president to fulfill his constitutional responsibility and ample time for the Congress to fulfill their constitutional responsibility,” Press Secretary Josh Earnest said Monday, according to the Hill. Scalia was known as a linchpin of the court’s conservative wing, and Obama’s decision not to attend his funeral Saturday earned the ire of many Republicans.