The White House has moved to put a lid on speculation that U.S. President Donald Trump might fire the special counsel investigating the Russia affair, while leaving just enough of a crack to keep the idea bubbling.

A presidential spokesperson responded with a qualified endorsement Tuesday: "While the president has the right to [fire Robert Mueller], he has no intention to do so," Sarah Huckabee Sanders said in response to a reporter's question.

That response came after a sudden burst of chatter about Mueller's termination. It began over the weekend when Trump's lawyer wouldn't rule it out; then his associate Newt Gingrich appeared to call for it, as did some conservative commentators; Trump's friend Chris Ruddy said he was actually considering it.

A report in The New York Times said the president had indeed weighed the possibility, was dissuaded by staff, and has since landed on the idea of simply pressuring Mueller by letting him know he could be fired.

Pushback

A series of Washington power-players had pushed back Tuesday against the idea of firing Mueller.

That pushback came from top officials from the party's congressional wing, as well as from administration officials who actually have the legal authority over the special counsel and would need to be involved in any firing.

"I have confidence in Bob Mueller," said top House Republican Paul Ryan, in remarks echoed by top Senator Mitch McConnell. Ryan said: "I think the best thing to do is to let Robert Mueller do his job.... That, to me, is the smartest thing to do, the best thing to do."

The same goes for people in the administration.

Sessions promises not to get involved

That includes the man who hired the special counsel and would have to do the firing. The deputy attorney general, a civil servant, assured a congressional committee he would resist an unwarranted dismissal order: "I'm not going to follow any order unless I believe they are lawful and appropriate orders. It wouldn't matter to me what anybody said," Rod Rosenstein testified.

The reason the deputy attorney general is in charge is his boss has recused himself.

And that boss, Jeff Sessions, also promised Tuesday not to get involved in any firing. For one thing, the attorney general testified in a separate congressional hearing: "I have confidence in Mr. Mueller."

He also said it would be inappropriate for him to get involved — given that he has recused himself from Russia-election-related matters. When his opponents pointed out that his recusal didn't stop him from participating in the firing of James Comey, he insisted the Comey firing was done for other reasons.