The Axe Files, featuring David Axelrod, is a podcast distributed by CNN and produced at the University of Chicago Institute of Politics. The author works at the institute.

(CNN) Former Senate Majority Leader Trent Lott says he would have taken up President Obama's nomination to fill the seat of the late Supreme Court Justice Antonin Scalia.

The president has yet to name his pick, but current Senate Majority Leader Mitch McConnell has announced that he will not take up any nomination for the vacancy created by Scalia's death last month, arguing that it should be up to the next president to fill.

"I probably would've handled it differently," Lott told CNN senior political commentator David Axelrod on "The Axe Files" podcast, produced by CNN and the University of Chicago Institute of Politics. "My attitude, particularly on the Supreme Court, was that elections do have consequences, sometimes bad, and I tried to lean towards being supportive of the President's nominees, Democrat or Republican."

"If they were qualified by education, experience, and demeanor and had no other side problem, my predisposition was to be for them," added the Mississippi Republican, who led the Senate from 1996 to 2001.

Lott, now a prominent Washington lobbyist, qualified his comments by saying he understood McConnell's reluctance to entertain the nomination.

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