J. Scott Applewhite/Associated Press Would an Obama Supreme Court nominee smell bad or something? Senate Republican leaders say they won't even meet with whoever it is.

WASHINGTON -- Senate Republicans on Tuesday launched an unprecedented blockade of President Barack Obama's yet-to-be-named Supreme Court pick, saying they won't give any nominee a hearing or even meet with the candidate.

"I don't know how many times we need to say this," Senate Majority Leader Mitch McConnell (R-Ky.) told reporters. "The Judiciary Committee has unanimously recommended to me that we not hold a hearing. I don't know the purpose of such a visit. I would not be inclined to take one myself."

Supreme Court nominees typically make courtesy calls to senators, so that lawmakers can get to know them on a more personal level and question them in a more intimate setting.

But on Tuesday, at least five senior Republican senators -- McConnell, John Barrasso (Wyo.), John Cornyn (Texas), Orrin Hatch (Utah) and Lindsey Graham (S.C.) -- said they won't participate in this tradition for an Obama nominee.

"There'd be no reason to," Barrasso told HuffPost, when asked if he'd meet with whatever nominee Obama sends to the Hill.

"I don't see the purpose," Cornyn said.

"Joe Biden. Chuck Schumer. If they were in charge they'd be doing the exact same thing," Graham added. "I'm not going to meet with the nominee. I'm sure they'll be a nice person."

McConnell's comments came after every Republican on the Judiciary Committee signed onto a letter saying they won't give a hearing to Obama's pick. Court nominees have to clear this committee before they can get a Senate confirmation vote, so without action here, literally nothing can happen.

"Because our decision is based on constitutional principle and born of a necessity to protect the will of the American people, this Committee will not hold hearings on any Supreme Court nominee until after our next President is sworn in on January 20, 2017," reads the letter.

It's signed by Cornyn, Graham and Hatch, as well as GOP Sens. Chuck Grassley (Iowa), Jeff Sessions (Ala.), Mike Lee (Utah), Ted Cruz (Texas), Jeff Flake (Ariz.), David Vitter (La.), David Perdue (Ga.) and Thom Tillis (N.C.).

Flake ducked questions about whether he thought the GOP blockade on Obama's nominee, sight unseen, could blow up in their faces.

"I'll let Sen. Grassley, the chairman, talk about it," Flake said, walking quickly down a Senate hallway. "I want to let him talk about it."

McConnell announced his intent to block any Obama nominee soon after news broke of the death of Justice Antonin Scalia. He said he wants the next president to choose Scalia's replacement -- hoping, of course, that a Republican will win the 2016 election.

"The overwhelming view of the Republican conference in the Senate is that this vacancy should not be filled by this lame duck president," McConnell reiterated Tuesday afternoon.

A few senators, however, have broken with this hard-line position and said they'd be willing to look at an Obama nominee. Even under normal order, however, it will be an uphill climb; an Obama nominee would need to get the support of every single Democratic senator and at least 14 Republican ones to get confirmed.

Democrats have shot back that it would be unprecedented to not even consider a president's Supreme Court nominee and have vowed to make Republicans pay in November.

"The party of Lincoln is becoming the party of Donald Trump," Senate Minority Leader Harry Reid (D-Nev.) responded Tuesday, referring to the divisive 2016 GOP front-runner. He also predicted that Grassley would "go down in history as the most obstructionist Judiciary chair" for blocking a hearing.

Sen. Roger Wicker (R-Miss.), however, said he's confident their strategy of obstruction will pay off.

"Let me just say, we are very comfortable letting the American people speak on this issue," the senator said.