Senate Majority Whip John Cornyn said Tuesday there’s a chance the Senate will actually vote on legislation designed to protect Special Counsel Robert S. Mueller III.

The Republican from Texas suggested that may be the price paid in order to get an agreement with retiring Republican Sen. Jeff Flake of Arizona to let more of President Donald Trump’s judicial nominations through the Judiciary Committee.

Flake has stated he will oppose judicial nominations until there is a path forward for voting on the Mueller-related legislation, which would create legal opportunities for special counsels to contest inappropriate dismissals.

With a one-seat GOP advantage on the Judiciary Committee, Flake’s opposition makes the path through committee more complicated, but not impossible.

“We’re going to be working with Senator Flake to see what he needs in order to lift his hold,” Cornyn said. “There is a possibility we will have a vote on the Mueller, so-called Mueller protection bill, but I think there really is some serious constitutional issues on that, and I certainly don’t support it.”

Cornyn, who is not alone among Senate Republicans in having constitutional concerns about the bipartisan legislation, made the comments during an interview with conservative radio host Hugh Hewitt.

“I don’t think the president’s going to fire Bob Mueller, but we have a farm bill to take care of. There’s a lot of interest in a criminal justice reform bill. We have a Yemen war powers resolution that’s privileged and needs to be voted on this week, probably. So we’ve got a lot to do and not much time to do it in,” Cornyn said.

Senate Minority Leader Charles E. Schumer of New York reaffirmed Monday that Democrats would seek to include a form of the bill as a rider in the upcoming must-pass spending legislation if there isn’t a vote on the measure before then.

“We need to come together here in the Senate — Democrat and Republican — to pass legislation to protect the special counsel’s investigation. We already have the bill. It’s bipartisan — two Republicans and two Democrats. It has passed committee on a bipartisan vote,” Schumer said on the Senate floor. “If the majority leader refuses to give it the vote that it deserves, Democrats will push to include it in the must-pass spending bill that we must approve in the next few weeks.”

Cornyn later told reporters at the Capitol that Senate Republicans would be conducting a whip count on the special counsel protection measure to try to get clarity on the next steps.

“We are whipping the bill to see where people are, to give us an idea of what the outcome would be. I think it’s an unconstitutional bill and forgets the lessons we’ve learned from independent counsel in the past, like with Watergate and not just Watergate but the Clinton-era with Ken Starr and others. There was sort of bipartisan agreement to let the independent counsels bill lapse. And so this, I think, forgets to remember some of those lessons,” Cornyn told reporters. “But, it’s the leader’s call.”

Watch: Senate Republicans Talk Leadership Team and Special Counsel Protections