Senate Republicans are measuring support for legislation protecting special counsel Robert Mueller Robert (Bob) MuellerCNN's Toobin warns McCabe is in 'perilous condition' with emboldened Trump CNN anchor rips Trump over Stone while evoking Clinton-Lynch tarmac meeting The Hill's 12:30 Report: New Hampshire fallout MORE and could bring the bill up for a vote, Sen. John Cornyn John CornynQuinnipiac polls show Trump leading Biden in Texas, deadlocked race in Ohio The Hill's Campaign Report: GOP set to ask SCOTUS to limit mail-in voting Liberal super PAC launches ads targeting vulnerable GOP senators over SCOTUS fight MORE (Texas), the No. 2 Senate Republican, said Tuesday.

Cornyn, in separate interviews with reporters and conservative radio host Hugh Hewitt, said Republicans could give the legislation a vote as they try to defuse a fight with Sen. Jeff Flake Jeffrey (Jeff) Lane FlakeHow fast population growth made Arizona a swing state Jeff Flake: Republicans 'should hold the same position' on SCOTUS vacancy as 2016 Republican former Michigan governor says he's voting for Biden MORE (R-Ariz.) that is holding up dozens of judicial nominees.

"We're whipping that to see where people are. I think the leader needs that information to decide how to manage all the competing demands on our time," Cornyn said when asked about discussions within the Republican caucus about the legislation.

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Flake has pledged to vote against all of President Trump Donald John TrumpSteele Dossier sub-source was subject of FBI counterintelligence probe Pelosi slams Trump executive order on pre-existing conditions: It 'isn't worth the paper it's signed on' Trump 'no longer angry' at Romney because of Supreme Court stance MORE's judicial nominees until he gets a vote on the legislation. With Republicans holding an 11-10 majority on the Senate Judiciary Committee, Flake's tactics effectively block them from moving nominees to the full Senate unless they can get help from Democrats.

Cornyn said Republicans were willing to hold a vote on the legislation "if that's what it's going to take" to move nominees. But, asked if it was a realistic possibility, he said leadership was still measuring support to get "an idea of what the outcome would be."

Republicans have put a premium on confirming Trump's judicial picks, which they view as one of their best shots at having a long-term impact on the direction of the country.

Republicans have been privately mulling having a vote related to the legislation after Flake warned earlier this month that he would oppose all judicial nominees until the Mueller bill is brought up on the Senate floor.

In addition to effectively blocking nominees at the committee level, it also forces Republicans, who currently have a 51-49 majority, to lean on Vice President Pence to break a tie if no Democrats support a nominee.

Cornyn told Hewitt that Republicans were discussing a vote on the legislation and there was a “possibility” the Senate could give it a vote.

“We are checking with our members now to see exactly where, you know, how it would come out. It may be that he does get that opportunity,” Cornyn said, adding that he does not support it and believes the legislation has constitutional issues.

The Judiciary Committee passed legislation that would protect Mueller, or any other special counsel, in the event he is fired, but the bill has stalled amid opposition from GOP leadership.

The bill would codify Justice Department regulations that say only a senior DOJ official can fire Mueller or another special counsel.