Legislative efforts to shield special counsel Robert Mueller from political interference appear to have stalled out on Capitol Hill, even as attempts from President Donald Trump and his allies to discredit the investigation intensify.

On a day when the special counsel’s probe handed down its first indictments, even one of the authors of legislation aimed at shielding Mueller from political prying seemed to back away from it.

“I don’t feel an urgent need to pass that law until you show me a reason that Mr. Mueller is in jeopardy,” Sen. Lindsey Graham (R-S.C.), who introduced a bill alongside Sen. Cory Booker (D-N.J.) in August, told The Daily Beast. “I don’t think anybody in their right mind at the White House would think about replacing Mr. Mueller unless there was a very good reason.”

Trump has flirted with the idea of firing Mueller in the past, and lawmakers expressed concern on Monday that the indictments targeting two former Trump campaign officials—and the guilty plea of a third—would spur new efforts to upend the probe. As Paul Manafort, Rick Gates and George Papadopoulos were revealed as Mueller’s first targets, Trump’s former strategist Stephen Bannon plotted “a much more aggressive legal approach short of firing Mueller,” a source close to Bannon told The Daily Beast.

Some lawmakers on Capitol Hill are fearful. Sen. Mark Warner (D-VA) and Rep. Adam Schiff (D-CA), the top Democrats on the Senate and House intelligence committees, respectively, issued vague calls for bipartisan action to insulate Mueller and his investigation from political interference. But few Democrats mentioned the two pieces of legislation that have been introduced to do exactly that.

Sen. Chris Coons (D-DE) has joined forces with Sen. Thom Tillis (R-N.C.) on a separate bill that would allow Mueller, if he were fired, to challenge his termination in front of a panel of three federal judges who would then decide within two weeks whether his firing was justified.

In a discussion with reporters on Monday, Coons said that Monday’s indictments underscored the importance of ensuring that Mueller can continue his investigation unimpeded.

But he also acknowledged that his legislation appears to be going nowhere—at least for now. Coons and Tillis have not yet sat down with Graham and Booker to reconcile their two pieces of legislation into one, and the senators don’t yet have a commitment from Republican leaders on either a markup or a floor vote. One such leader, Senate Majority Whip John Cornyn (R-TX) told The Daily Beast that Mueller “knows what to do, and he’s doing it,” and that Congress should stay in “our lane.”

Even the most vehement critics of the president said on Monday that they didn’t view legislation as a necessary step to protect Mueller, arguing that Trump was not cavalier enough to take the risk of dismissing the special counsel or disbanding his investigation.

“I can’t even imagine any administration taking a move like that,” Sen. Bob Corker (R-TN), who recently suggested that Trump was setting the U.S. on a path to World War III, told The Daily Beast. “That would be going a step further than I could possibly imagine.”

Sen. Jeff Flake (R-AZ), who disparaged Trump during a speech on the Senate floor last week in announcing his retirement, said it was too early to tell whether legislation is needed.

“It depends on how the president reacts,” Flake told The Daily Beast. “There’s no indication that he’s going to go in and fire or pardon at this point.” When asked if he would back legislation, Flake quipped: “We’ll see.”

In taking the Trump administration at its word that it has no plans on dismissing Mueller, these two senators—along with the majority of their GOP colleagues—are running a risk, Democrats argue. If Trump does opt to fire the special counsel, it would set off an intense political backlash. But, absent pre-existing legislation, it would be within his purview to direct Deputy Attorney General Rod Rosenstein to do so and to fire Rosenstein if he didn’t comply.

On Monday, White House Press Secretary Sarah Sanders said Trump has “no intention or plan” to fire Mueller. But the administration’s allies have already put on the pressure. In recent months, Trump and those close to him left the door open to shutting down Mueller’s investigation, describing it as a political witch-hunt. When Trump suggested Mueller would be crossing a line if his investigation included the president's personal finances, Republicans and Democrats on Capitol Hill issued a blunt warning to Trump that it would be politically toxic if he does anything to interfere with the probe.

Mueller’s credibility and integrity are viewed, in large measure, as rock solid by lawmakers across the political spectrum.

“I think the message has been very clear—not just today, but over the last few weeks—is the number of Republican members of Congress who have said he is approaching this in a professional way,” Sen. Ron Wyden (D-OR) said. “And again, I think today was the textbook case of professionalism by Bob Mueller.”

But not even Wyden—one of the president’s fiercest critics when it comes to the Russia investigations—committed to supporting legislation to protect the special counsel.

“I continue to believe that current law says you can only dismiss an individual like this for cause,” Wyden said. I’m also willing to look at the legislation, but that’s current law that you have to have cause.”