One of the first Senate Republicans to call for legislation protecting special counsel Robert Mueller has stopped actively pushing that effort, sources on Capitol Hill say.

Sen. Thom Tillis, a North Carolina Republican in his first term, made headlines over the summer when he signed on to legislation with Sen. Chris Coons (D-DE) that would have shielded Mueller from being fired. But Tillis has largely abandoned the push to move that legislation forward while conceding that the bill doesn’t have the support to get through Congress. His office says he still supports the bill, but that the matter isn’t urgent since Trump says he doesn’t plan to fire Mueller.

“[T]he chatter that the administration is considering removing Special Counsel Mueller has completely come to a halt,” Tillis spokesperson Daniel Keylin said in an email to The Daily Beast. “In fact, the president and his administration have spoken favorably of Special Counsel Mueller’s professionalism and integrity, and recent reports indicate the investigation may soon come to an end.”

On Thursday night, The New York Times reported that Trump tried to fire the special counsel last summer. Keylin told The Daily Beast that despite the revelation, Tillis continues to trust that the president isn’t planning to fire Mueller, who is leading an investigation into potential coordination between the Trump campaign and the Russian government during the 2016 election.

“ Chatter that the administration is considering removing Special Counsel Mueller has completely come to a halt. ” — Tillis’ spokesperson

Keylin noted that his boss didn’t start pushing for a bill to protect the special counsel until after Trump reportedly tried to fire him. Tillis introduced his bill with Coons in August, while Trump tried reportedly to fire Mueller in June. Those who are arguing that a firing is imminent, Keylin added, were trying to score political points.

“As Senator Tillis has repeatedly said, Special Counsel Mueller is a career professional respected by both sides of the aisle for good reason,” Keylin wrote. “He should be able to do his job without elected officials trying to score cheap political points for their own partisan gain.”

The Tillis-Coons legislation isn’t the only bill designed to shield Mueller from Trump. Sens. Lindsey Graham (R-S.C.) and Cory Booker (D-N.J.) have one of their own.

Keylin noted that there is a substantive difference between Graham-Booker and Tillis-Coons, regarding when the special counsel would be able to ask a judge to shield an inquiry, which is reconcilable. And he said the bill’s supporters needs to address constitutional concerns some members have. He also said the bill “currently does not have” enough support to pass.

Lawmakers are working to merge the two bills. But those negotiations have stalled.

Tillis’s spokesman noted that he still thinks the bill should ultimately become law. But the dialing back of the Senator's support is significant. Unlike Graham, who veers between bashing Trump and golfing with him, and Coons and Booker—both Democrats—Tillis could bring the legislation to shield Mueller serious bipartisan bona fides. When he introduced his bill, Tillis similarly didn’t believe that a firing of Mueller was near, but he pitched the legislation as a precautionary measure.

“I don’t have any evidence to suggest the White House had any intention of doing it [firing Mueller], but it’s a helpful way for us to take it off the table,” he explained.

While Tillis has decided to step back from the legislative push, his would-be cosponsors said passage is now more urgent than ever, even before reports of Trump trying to axe Mueller.

“We continue to see news reports week in and week out that suggest that the president has engaged in inappropriate attempts to influence the investigation,” Coons told The Daily Beast on Wednesday, speaking before the Times story broke. “I just may have a different assessment of its urgency.”

Sen. Cory Booker—frequently listed as a potential 2020 presidential candidate—echoed Coons’ sentiment, after Wednesday votes and before the Times story dropped.

“It’s always the right time to do what’s right,” he told The Daily Beast.

This post has been updated for clarity.