In an interview with CNN's Dana Bash on "State of the Union" Sunday, the Kentucky Republican stuck by his stance that Obama's successor ought to fill the vacancy created by the death of Justice Antonin Scalia.
"I can't imagine that a Republican majority Congress in a lame duck session after the American people have spoken would want to confirm a nominee opposed by the NRA, the NFIB, and the New York Times says would move the court dramatically to the left," McConnell said. "This nomination ought to be made by the next president."
He also criticized Garland, arguing that opposition to his nomination from the National Rifle Association and the National Federation of Independent Businesses shows he's too liberal.
Asked if he's ruling out the possibility of a lame duck confirmation entirely, McConnell said: "Yes."
Democrats are prodding the GOP to give Garland a confirmation vote.
Senate Democratic leader Harry Reid of Nevada called on Republicans to "man up and do it now" in an appearance on NBC's "Meet the Press." He also predicted that McConnell will back off his pledge not to give Garland a vote.
"Mitch McConnell has said a lot of things. But his Republican senators are not going to go over that cliff with him. They're not going to do it. As I told Merrick Garland, 'This is going to break. You're going to become a Supreme Court justice.' "
Reid added: "And in addition to the people agreeing to meet, we have Republican senators and a veteran senator who said, 'Well maybe what we should do is do it in a lame duck.' Orrin Hatch, Lindsey Graham, others have said that. But if they're going to do it in lame duck, do it now."
The GOP's front-runner is currently Donald Trump -- but McConnell predicted Trump wouldn't be a drag on Republican candidates.
"All of those races will be run by candidates seeking to appeal to the voters in those states. Senate races are statewide races -- you can craft your own message for your own people," he said.
Still, asked about the violence at Trump rallies, McConnell said candidates should encourage rally attendees to engage in "peaceful discourse" and that doing so "would be a very important addition to the conversation."