Updated at 2:33 p.m. ET

Key Republican senators on the Judiciary Committee emerged from a closed door meeting in Majority Leader Mitch McConnell’s office Tuesday united in their determination not to consider any nominee to replace Antonin Scalia until the next president takes office.

Tuesday was the first full day the Senate was back in session since Scalia’s death Feb. 13.

“We believe the American people need to decide who is going to make this appointment rather than a lame duck president,” said Majority Whip John Cornyn (R-TN).

When asked if they would start the process after the new president took office or if they would consider doing it in the lame duck session, Cornyn replied “No, after the next president is selected. That way the American people have a voice in the process.”

The Republican members of the Judiciary Commitee were unanimous in agreeing not to move forward with any Obama nominee for the Supreme Court, said Cornyn, who was in the meeting. Sen. Bob Corker (R-TN), who was not in the meeting, later said that GOP senators were told at their weekly lunch that the Judiciary Committee Republicans were in unanimous agreement on the strategy.

Meanwhile, Judiciary Committee Chair Charles Grassley (R-IA) and the rest of the committee Republicans sent a letter to McConnell outlining their plan to block any Obama nominee for Scalia’s seat.

Sen. Lindsey Graham (R-SC) said that “there’s no use starting a process that’s not going to go anywhere and we are going to let the next president decide,” when asked why there would be no hearings.

When TPM asked if he had political concerns about the decision not to move forward with a nominee, Graham responded.”I have zero concerns politically.”

“I think this is what they would do,” Graham said referring to Senate Democrats. “For them to say they wouldn’t do this is a lie.”