Special Counsel Robert S. Mueller III testifies during a May 16, 2013, Senate hearing when he was the FBI director. (Brendan Smialowski/AFP/Getty Images)

On its face, the idea seemed as startling as it was preposterous: A president firing a special counsel appointed to investigate his campaign’s possible role in Russia’s interference with the 2016 U.S. election.

But this president is Donald Trump, who speculates about firing people as sport and who dispatched two key officials connected to the probe of Russia’s election meddling during his first five months in office.

To some of Trump’s most loyal allies, terminating Robert S. Mueller III as special counsel of the expanding Russia investigation is a tantalizing idea — one that has gained currency on the right and, according to one of Trump’s friends, has been considered by the president himself.

After Christopher Ruddy, a Trump friend and president of the conservative media outlet Newsmax, said on PBS’s “News Hour” Monday night, after visiting the White House, that the president was “weighing” firing Mueller, official Washington on Tuesday sounded a collective and resounding call: Do not do it.

“I think the best thing to do is to let Robert Mueller do his job,” House Speaker Paul D. Ryan (R-Wis.) said. “I think the best vindication for the president is to let this investigation go on independently.” Ryan went on to say that the discussion about a possible firing amounted to a mere “rumor.”

White House press secretary Sean Spicer sought to undermine Ruddy’s credibility by pointing out that Ruddy had not met directly with the president during his Monday visit.

“Chris Ruddy speaks for himself,” Spicer said.

Trump has been counseled strongly against trying to remove Mueller and appears unlikely to take such a drastic step, according to White House officials and other people close to the president.

But neither Spicer nor other Trump aides would explicitly dispute Ruddy’s assertion that the president has considered firing Mueller.

“While the president has a right to, he has no intention to do so,” principal deputy White House press secretary Sarah Huckabee Sanders told reporters aboard Air Force One on Tuesday night.

All day, Trump repeatedly declined to put the issue to rest.

President Trump walks with his daughter Ivanka Trump from the Oval Office to board the Marine One helicopter for a trip to Milwaukee on Tuesday. (Jabin Botsford/The Washington Post)

Reporters asked Trump four times during a health-care meeting at the White House whether Mueller should be fired, and the president gave no answer. They asked again as he walked across the South Lawn to board the Marine One helicopter, and again he gave no answer. Reporters asked once more as Trump stepped off Air Force One in Milwaukee, and once more he had no answer.

“If Trump fired Mueller, it would be an act of uber hubris never seen before in American history,” said Douglas Brinkley, a presidential historian at Rice University. “It would pale, compared to what Nixon did with the firing of Archibald Cox. . . . We would be in a constitutional crisis.”

Brinkley was referring to the “Saturday Night Massacre” of 1973, when President Richard M. Nixon sought to order his attorney general to fire Cox, who had been serving as the independent special prosecutor overseeing the Watergate investigation.

How or even whether Trump could fire Mueller was the subject of debate among legal and political experts on Tuesday.

Trump last month fired FBI Director James B. Comey, who had been overseeing the Russia probe before the appointment of a special counsel. Earlier in his term, Trump fired acting attorney General Sally Q. Yates after she warned the administration that national security adviser Michael Flynn had misled the White House about his contacts with Russian officials.

But the termination of the special counsel would be more complicated. It ordinarily would fall to the attorney general, but Attorney General Jeff Sessions recused himself from Russia matters after he was found to have misled the Senate during his confirmation hearing about his contacts with Russian Ambassador Sergey Kislyak. Thus the decision to fire Mueller would fall to Deputy Attorney General Rod J. Rosenstein, who appointed Mueller to the job last month.

In a Tuesday appearance before the Senate Appropriations Committee, Rosenstein described Mueller as operating independently from the Justice Department in his investigation and said that if Trump ordered him to fire Mueller, he would comply only if the request were “lawful and appropriate.”

“I’m not going to follow any orders unless I believe those are lawful and appropriate orders,” Rosenstein said. He added later: “As long as I’m in this position, he’s not going to be fired without good cause,” which he said he would have to put in writing.

“If there were good cause, I would consider it,” Rosenstein testified. “If there were not good cause, it wouldn’t matter to me what anybody says.”

Later Tuesday, Sessions appeared before the Senate Intelligence Committee, and Sen. Mark R. Warner (D-Va.) asked the attorney general whether he has confidence in Mueller.

“I have known Mr. Mueller over the years,” Sessions said. “He served 12 years as FBI director. I knew him before that. And I have confidence in Mr. Mueller.”

But, Sessions added, “I am not going to discuss any hypotheticals or what might be a factual situation in the future that I’m not aware of today, because I know nothing about the investigation and fully recuse myself.”

When Warner asked whether Sessions believed Trump had confidence in Mueller, the attorney general said: “I have no idea. I’ve not talked to him about it.”

The notion of dismissing Mueller has been bubbling on the political right in recent days, as Trump supporters grow weary of an expanding investigation that the president considers to be an illegitimate political “witch hunt.”

Ruddy’s PBS interview came a day after Jay Sekulow, a prominent conservative attorney who has been informally advising Trump, left open the possibility that Trump could decide to remove Mueller, in a Sunday interview on ABC News’s “This Week.”

Asked by anchor George Stephanopoulos whether Trump would promise not to attempt at any time to order Rosenstein to fire Mueller, Sekulow said, “Look, the president of the United States, as we all know, is a unitary executive.”

Sekulow added that “the president has authority to take action. Whether he would do it is ultimately a decision the president makes. I think that’s complete conjecture and speculation.”

Ruddy said in an interview with The Washington Post on Tuesday that he based his comments to PBS largely on Sekulow’s statement. “I think it’s a smart thing to have it as an option,” Ruddy said of firing Mueller, though he added, “I personally don’t think it’s a wise thing to do.”

Ruddy said White House aides became agitated with his comments to PBS and said Spicer sought his help Monday night with damage control as news organizations cited Ruddy’s statement in reporting that the president was considering firing Mueller.

“Sean called me last night and asked me to qualify what I was saying, that I did not speak to the president,” Ruddy said. “I said, ‘I never claimed I spoke to the president, so why would I issue a statement saying I didn’t speak to the president?’ ”

Ruddy added: “It’s amateur hour over there. . . . It’s amazing to me that the White House press office has done such a poor job exposing the special counsel and defending the president.”

This is not the first time Ruddy has wreaked havoc for the West Wing with his suggestions about who may be in Trump’s crosshairs. In February, after having a drink with the president at Mar-a-Lago — Trump’s private resort in Palm Beach, Fla., where Ruddy is a member — Ruddy told The Post and other news organizations that White House chief of staff Reince Priebus was “in way over his head.”

Plenty of other Trump supporters on the outside have been stoking a “Fire Mueller” campaign. Former House speaker Newt Gingrich tweeted Monday that it was “time to rethink” the special counsel’s investigation, while talk radio hosts including Rush Limbaugh and Mark Levin have endorsed the idea of Trump dismissing him.

Roger Stone, a former Trump consigliere and political adviser, tweeted Tuesday: “Mueller is a establishment neocon ringer and Comey crony — and the fix is in to falsely indict @realDonaldTrump for obstruction.”

Democrats on Tuesday called for an end to the right-wing trash talk about Mueller and said the special counsel must be left alone to pursue his investigation.

“The effort to suppress it, to smear Mueller, to call it a ‘witch hunt,’ is part of a calculated and orchestrated effort, in my view, to undermine justice and the credibility of this investigation,” Sen. Richard Blumenthal (D-Conn.) said on MSNBC’s “Morning Joe.”

Rep. Adam B. Schiff (D-Calif.) said it seemed ridiculous that Trump would seriously consider ordering Mueller’s removal.

“I have to think this is just the president venting,” said Schiff, also on “Morning Joe.” “But then again, I remember talking about whether I thought there was any chance that the president would fire Comey, and that didn’t seem possible, either.”

Sari Horwitz and Matt Zapotosky contributed to this report.