Alabama Sen. Tommy Tuberville and a group of his fellow GOP senators are plotting a new tactic to break the Senate's gridlock on stalled military nominees: they may force a procedural vote on the Marine Corps commandant nominee, in a breach of Senate protocol.

Senators huddled behind closed doors in Senate Minority Leader Mitch McConnell's office to discuss taking the unusual step. It is extremely rare for a rank-and-file member to force a procedural vote -- that is usually left to the Senate majority leader, due to concerns that normalizing this in the minority could make the already cumbersome Senate even more difficult to manage.

With the effort, Republican are seeking to shift the blame in the growing feud over Tuberville's block on Pentagon nominations to Senate Majority Leader Chuck Schumer, who has refused to put individual nominees on the floor over concerns about the Alabama Republican's tactics. The Democratic leader has argued that such nominations have long been quickly confirmed in the Senate by voice votes and doing otherwise would set a damaging precedent in the chamber.

"It's unusual, but it's where members are," said South Dakota Sen. John Thune, citing "pent up frustration," because "Schumer won't allow a vote." He added, "I don't know where it goes from here, but at least this is one way of breaking things."

It's the latest development in a monthslong blockade by Tuberville over his demands that the Pentagon scrap its policy providing a travel allowance for troops and their families who must travel to receive an abortion because of the state laws where they are stationed. Tuberville argues the policy is illegal and should be up for a vote in Congress, while Pentagon officials have pointed to a Justice Department memo that says the policies are lawful.

But with the Pentagon and Tuberville not budging, GOP senators are looking to take matters into their own hands.

Schumer has refused to schedule a vote on any of the nominees out of concerns that giving into Tuberville could incentivize other senators to place holds to achieve their policy objectives. He has instead demanded that Tuberville drop his blockade and allow the nominations to quickly be confirmed by voice vote.

The process that Tuberville is trying to use involves him collecting 16 other signatures on a petition -- at that point he could file the petition to set up a procedural vote, which would require 51 votes to succeed. Thune believes Tuberville has enough support to at least force the vote.

"I didn't sign it," Thune said. "He's got the -- I think he's got the requisite number of signatures. We'll see where it goes. I mean, I think there were other ways of getting this done, but he was intent on pursuing a cloture petition, to use that mechanism. So we'll see where it lands."

Sen. John Cornyn said that he has not signed on, but he will. "I haven't yet, but I intend to," the Texas Republican told reporters. Sens. Lindsey Graham of South Carolina and Marco Rubio of Florida added that they had signed the petition.

It is unclear how this will play out, and Schumer has tools at his disposal to undercut Tuberville's tactics.

Alaska Sen. Dan Sullivan was close to using this same process to force a vote on one of the military nominees before the August recess, but at the time, McConnell helped talk him out of doing it due to its implications for the Senate.