President Donald Trump’s allies have been pushing the rumor that he might fire special prosecutor Robert Mueller. Much of the rest of Washington is trying to knock it down.

On Tuesday, Deputy Attorney General Rod Rosenstein said he knows of no reason to oust Mueller, who is overseeing the FBI’s probe into Russian meddling in the election and possible collusion between Trump’s campaign and the Kremlin. He added that he would resist any inappropriate calls from Trump to remove him.

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House Speaker Paul Ryan (R-Wis.) said he has “confidence” in Mueller and delicately warned Trump against firing him. "The best advice would be to let Robert Mueller do his job,” Ryan told reporters.

Sen. Dianne Feinstein (D-Calif.) predicted dire consequences if Trump made such a move. "I do believe it would be catastrophic, and I do believe it would destroy any shred of trust in the president’s judgment that remains over here,” she said at an appropriations hearing.

And, after Newsmax CEO and Trump ally Chris Ruddy threw the rumor mill into overdrive on Monday evening by saying Trump was thinking about firing Mueller, Newt Gingrich — another prominent surrogate — threw cold water on the idea.

Gingrich said he talked with Trump on Monday night, and he offered a flat “no” when asked whether he believed Trump would dismiss Mueller. “The president actually is pretty confident that ultimately this is all going to come out in the wash and ultimately he's still going to be president and this stuff’s all going to go away,” Gingrich said on CBS.

But even as prominent Washington figures bat down the idea that Mueller could be shown the door, the debate is still aiding the White House’s efforts to try to discredit the former FBI director and push the idea that the sprawling Russia probe is a vendetta against Trump.

While White House aides are saying Trump has no plans to fire Mueller, his surrogates have been pointedly questioning Mueller’s ability to fairly do his job. They’re noting that fired FBI Director James Comey — potentially one of his chief witnesses — is a longtime friend and that some of Mueller’s newly appointed prosecutors have given money to Hillary Clinton and Barack Obama. The whole idea of the investigation is flawed, they say.

Some of the most forceful pushback on Tuesday came from Rosenstein, who — unlike Trump — has the direct power to fire Mueller.

“I’m not going to follow any orders unless I believe they are lawful,” Rosenstein testified before the Senate Appropriations Committee about potential directives from Trump.

Rosenstein told lawmakers that he knew of no reason to date to fire Mueller. “Director Mueller is going to have the full degree of independence he needs to conduct the investigation appropriately,” he added.

Trump can’t fire Mueller directly but could, in theory, order Rosenstein to do so and dismiss the deputy attorney general if he didn’t comply. That would then allow the president to seek out someone who would obey his order to terminate Mueller.

Rosenstein suggested he would be willing to take the hit, telling the committee that unless there were “good cause” to fire Mueller, “it wouldn’t matter what anybody said.”

Comey told lawmakers last week in his first public comments since his firing that Trump had asked him to “lift the cloud” of the Russia investigation and said he believed he was let go because of the probe.

Rosenstein was a key figure in Comey’s dismissal, drafting a memo that justified his firing by pointing to Comey’s unusually public statements about the Hillary Clinton email probe. But while the White House initially tried to pin the idea for the ouster on Rosenstein and other DOJ officials, Trump himself later said the cloud of the Russia probe influenced his decision to fire Comey.

Sen. Chris Van Hollen (D-Md.) on Tuesday pressed Rosenstein on whether Attorney General Jeff Sessions would be violating his recusal from the Russia probe if he fired Mueller. “I don’t expect that to happen, senator,” Rosenstein replied, eventually conceding that it was “probably fair” to say it would breach the recusal.

Van Hollen said he doubted Rosenstein would remove Mueller directly but feared that Trump might keep firing DOJ leaders until someone was willing to oust the special counsel.

“I’m worried about in those circumstances, the president [would] keep going until he found someone to take that action,” Van Hollen said.

Rosenstein also sidestepped a question about whether Mueller would be able to challenge any such dismissal in court. “I hope we never reach that point. That's like a law school hypothetical I’d be reluctant to answer without doing some research first,” he said.

Rosenstein rejected as remote most of the scenarios senators laid out. However, during an exchange with Sen. Joe Manchin (D-W.Va.), the deputy attorney general seemed to concede that his own firing wasn’t out of the question.

“Could you be terminated without cause?” Manchin asked.

“Yes,” Rosenstein replied, adding, “Anything’s possible, senator.”

“I understand. That’s what we know,” Manchin responded.

Josh Gerstein, Louis Nelson and Rachael Bade contributed to this report.