Sen. Chuck SchumerCharles SchumerSenate Dems step up protests ahead of ObamaCare repeal vote Senate Dems plan floor protest ahead of ObamaCare repeal vote Dem senator: Don't bet against McConnell on ObamaCare repeal MORE (D-N.Y.) is criticizing Senate Majority leader Mitch McConnellMitch McConnellSenate GOP delays ObamaCare repeal vote past recess The Hill's 12:30 Report Cruz, McConnell huddle with healthcare vote looming MORE for saying the Senate should not move forward with a Supreme Court nominee during President Obama's remaining months in office.

"You know, the kind of obstructionism that Mitch McConnell's talking about, he's harkening back to his old days. You know, he recently he said, 'Well, I want regular order,' " Schumer said on ABC's "This Week."

"But in 2010, right after the election or right during the election, he said, 'My number-one job is to defeat Barack ObamaBarack ObamaPoll: US favorability in world falls under Trump Dems face identity crisis Inspector general report: Park Service did not change records of crowd size at inauguration MORE,' without even knowing what Barack Obama was going to propose. Here, he doesn’t even know who the president's going to propose and he said, 'No, we're not having hearings; we're not going to go forward to leave the Supreme Court vacant at 300 days in a divided time,' " he said.

Schumer said that kind of strategy "isn't going to last," adding that the American people don't like obstruction.

He added that he thinks the president will nominate someone who is "mainstream."

"I believe that many of the mainstream Republicans, when the president nominates a mainstream nominee, will not want to follow Mitch McConnell over the cliff," he said.

"When you go right off the bat and say, 'I don't care who he nominates, I am going to oppose him,' that's not going to fly," he said.