Sen. Chuck SchumerCharles SchumerThe Hill's 12:30 Report Pelosi thanks GOP senators who voted against ObamaCare repeal Live Coverage: Senate votes down 'skinny' ObamaCare repeal MORE (D-N.Y.) is criticizing Senate Majority leader Mitch McConnellMitch McConnellMcCain urges 'a fresh start' on healthcare reform Obama spokesman: Congress needs 'political courage' to improve healthcare The Hill's 12:30 Report 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 ObamaBiden thanks GOP healthcare bill opponents after skinny ObamaCare repeal failure FDA gives cigar, e-cig makers more time to get products approved GOP lawmaker: Time for us to listen to Democrats on healthcare 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.