WASHINGTON -- When Senate Majority Leader Mitch McConnell (R-Ky.) decided that he would keep Antonin Scalia's Supreme Court seat vacant so the next president could decide, he might not have anticipated exactly how ugly the campaign was about to turn in his party.

But he knows now, and McConnell announced Tuesday that he's standing by his decision -- even going to the White House with Judiciary Committee Chairman Chuck Grassley to tell President Barack Obama so.

"We will reiterate that the American people will have a voice in the vacancy on the Supreme Court as they choose the next president, who in turn will nominate the next Supreme Court justice," McConnell said on the Senate floor.

“In other words, we will observe the ‘Biden Rule,’" he said, referring to a speech that the current vice president gave in 1992 in which he floated the idea of blocking a hypothetical nominee in President George H.W. Bush's final year.

McConnell also pointed to other more recent comments where Democrats toyed with the idea of obstructing Supreme Court nominees, although Democrats have responded that they never actually blocked nominations.

Democratic leaders also attended the meeting at the White House. Senate Minority Leader Harry Reid (D-Nev.) told reporters as he left that nothing came out of it.

How much progress was made at the WH meeting? Sen Reid: "Zero." #SCOTUS — Alex Rogers (@arogDC) March 1, 2016

McConnell and Grassley have decided they will not even hold hearings on the person Obama picks, let alone get to a vote.

“Americans have by now become well-acquainted with that advice from the vice president," McConnell said.

“Let’s use this meeting to discuss ways we can work together to make progress for our country, like tackling a drug crisis that’s tearing communities apart in all 50 states," he continued, pointing to legislation on the floor Tuesday. “I hope we’ll see that kind of cooperation continue. It’s important for our country."

For a look at how the Supreme Court blockade relates to what's happening in the campaign to choose the person McConnell is holding out for, watch the video above.