Key Republican senators vowed Tuesday not to vote or even hold a hearing on any Supreme Court nominee by President Obama to fill the seat of the late Justice Antonin Scalia -- a move likely to put the replacement process in a holding pattern, for now.

Though some GOP lawmakers appeared to waver in recent days in their opposition to considering a nominee, party leaders largely united Tuesday.

First, Senate Majority Leader Mitch McConnell said his party will not permit a vote. Then, every GOP member of the Senate Judiciary Committee penned a letter pledging not to even hold a hearing until the next president is sworn into office.

"[W]e wish to inform you of our intention to exercise our constitutional authority to withhold consent on any nominee to the Supreme Court submitted by this President to fill Justice Scalia’s vacancy,” they wrote in the letter to McConnell.

“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.”

When Republicans might ease their opposition is unclear. While the Judiciary Committee members want to wait until January, McConnell said Republicans won’t permit a vote on a nominee but would “revisit the matter” after November.

While McConnell acknowledged Obama can nominate a replacement, he said Republicans have a right to nix it -- and indicated he was also inclined to refuse a courtesy meeting with a nominee.

“Presidents have a right to nominate just as the Senate has its constitutional right to provide or withhold consent," the Majority Leader said in a speech on the Senate floor. "In this case, the Senate will withhold it."

“No hearing, no vote,” Sen. Lindsey Graham, R-S.C. told reporters after a meeting with McConnell.

"We believe the American people need to decide who is going to make this appointment rather than a lame-duck president," said Texas Sen. John Cornyn, also a member of the committee.

White House spokesman Josh Earnest called the Republicans' stance "unprecedented" but seemed to hold out hope that the Senate could hold hearings, pointing to a handful of lawmakers he said had expressed a willingness.

Democrats would appear to have few options. One of them, though, is for Democrats to try to force a floor vote on a nominee. It would still take 60 votes, however, to even proceed down that path, a steep climb considering Democrats have just 46 seats.

Republicans were fueled in part Tuesday by past remarks from Democrats who appeared to take a similar stance.

In McConnell's speech, the GOP Senate leader cited a 1992 speech by Vice President Joe Biden, who was then a Delaware senator, in which he said “once the political season is underway and it is, action on a Supreme Court nomination must be put off until after the election campaign is over.”

Although Biden was talking only hypothetically and there was no vacancy in 1992, Republicans have pointed to the speech as evidence of Democrats’ hypocrisy, and accused Biden of changing his tune depending on which party occupies the White House.

Scalia’s death on Feb. 13 has sparked a major political firestorm over whether Obama’s nominee for the seat on the court should even be considered with Minority Leader Harry Reid, D-Nev. accusing McConnell of taking his cue from Texas Sen. Ted Cruz and Donald Trump – who told a debate audience the chamber should “delay, delay, delay.”

Fox News’ Shannon Bream and Chad Pergram and The Associated Press contributed to this report.