Republicans are almost unanimous in the view that any move by President Trump Donald John TrumpBiden leads Trump by 36 points nationally among Latinos: poll Trump dismisses climate change role in fires, says Newsom needs to manage forest better Jimmy Kimmel hits Trump for rallies while hosting Emmy Awards MORE to fire special counsel Robert Mueller Robert (Bob) MuellerCNN's Toobin warns McCabe is in 'perilous condition' with emboldened Trump CNN anchor rips Trump over Stone while evoking Clinton-Lynch tarmac meeting The Hill's 12:30 Report: New Hampshire fallout MORE would be a political disaster.

Even GOP figures loyal to Trump see any such move as hugely counterproductive, while more critical conservative voices — especially those looking toward November’s midterm elections — fear the president would make already-difficult terrain close to impossible.

“I think it would be a really bad idea to fire him and exacerbate the situation,” said Barry Bennett, a senior adviser to Trump’s 2016 campaign who remains supportive of the president.

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Doug Heye, a former communications director of the Republican National Committee and a more critical voice, said the president and his party should fight Democrats on the grounds of “how many jobs were created, what is the unemployment rate and who gets the credit for it?”

Heye added dryly, “That is a much better place, as opposed to ‘did you or did you not obstruct justice?’ ”

Speculation about a possible push against Mueller from Trump has been feverish since FBI Deputy Director Andrew McCabe Andrew George McCabeGraham: Comey to testify about FBI's Russia probe, Mueller declined invitation Barr criticizes DOJ in speech declaring all agency power 'is invested in the attorney general' GOP votes to authorize subpoenas, depositions in Obama-era probe MORE was fired late Friday.

In the wake of the firing, the president took an even more combative tone than usual, name-checking Mueller in tweets for the first time and complaining that the special counsel’s team of investigators includes “13 hardened Democrats.”

Mueller himself has been reported to be a registered Republican, and he was nominated to lead the FBI by former President George W. Bush in 2001. There is, in any case, no prohibition on investigators holding different political views from the targets of their investigations.

But speculation about Mueller’s fate was stoked still further during the weekend when a Trump lawyer, John Dowd, told the Daily Beast that Deputy Attorney General Rod Rosenstein Rod RosensteinDOJ kept investigators from completing probe of Trump ties to Russia: report Five takeaways from final Senate Intel Russia report FBI officials hid copies of Russia probe documents fearing Trump interference: book MORE should “bring an end” to the probe.

Dowd, who initially told the Daily Beast he was speaking as Trump’s counsel, said later he was speaking only in a personal capacity.

Then, on Monday, news emerged that Trump is adding Joseph diGenova to his legal team. DiGenova has previously suggested the Justice Department and FBI are trying to frame Trump for collusion.

The president also maintained his Twitter fusillade, writing on the social media platform on Monday morning that the Mueller probe was “A total WITCH HUNT with massive conflicts of interest!”

The White House sought to dampen talk of a Mueller firing on Monday. Deputy press secretary Hogan Gidley told reporters during a trip to New Hampshire, “There are no conversations or discussions about removing Mueller.”

Michael Caputo, a longtime friend of the president who also worked on the 2016 campaign, painted Trump’s recent pronouncements as expressions of frustration rather than direct threats to Mueller.

“This is the president trying to define the terms of discussion when it comes to the investigation and perhaps even using Twitter to determine the boundaries,” Caputo said. “I don’t think he is threatening to fire anybody. I think he is frustrated and voicing his frustrations.”

Caputo, like other Trump loyalists, asserted that the root of this frustration lies in the length of time Mueller’s investigation has gone on, with no clear evidence of collusion with Russia made public.

White House lawyer Ty Cobb has said on previous occasions that Mueller’s probe would end by Thanksgiving 2017 or by the end of that year. Those predictions were widely interpreted as an attempt to keep Trump from losing his patience and taking Mueller on full force — but the downside of the strategy is now becoming clear.

The move to bring diGenova onto the team is being interpreted by some in Trump’s circle as a rebuke to Cobb and a break with his more conciliatory approach.

Caputo also emphasized, however, that another source of irritation for Trump, and for the administration more broadly, is the degree to which the Mueller probe overshadows everything else.

“Everyone’s extremely frustrated — those of us who … support the president and the people who want to get the agenda moving forward and they can’t,” he said.

Referring to Democrats and other Trump foes, Caputo added, “They have been stalling the president with this. They have successfully done so for over a year.”

But GOP voices more skeptical of Trump, such as Heye, argue the president makes his own trouble and distracts from his party’s priorities.

Alluding to the long-established practice of the Bureau of Labor Statistics releasing jobs numbers on the first or second Friday of each month, Heye said, “I look at the Friday jobs numbers and see these have been opportunities for really successful messaging by the White House. But we talk about the jobs report from about 8:30 to 8:33, and then we are back to whatever Trump is talking about — which is not that.”

Some Republican lawmakers have sought to promote a kind of halfway house between Trump’s red-hot anger at Mueller and the argument that the special counsel should simply be left to do his job unimpeded.

Conservatives in the House have suggested the appointment of a second special counsel who could investigate allegations of FBI and Department of Justice malfeasance. House Majority Leader Kevin McCarthy Kevin Owen McCarthyTrump asked Chamber of Commerce to reconsider Democratic endorsements: report The Hill's Morning Report - Sponsored by The Air Line Pilots Association - White House moves closer to Pelosi on virus relief bill Trump's sharp words put CDC director on hot seat MORE (R-Calif.) and House Majority Whip Steve Scalise Stephen (Steve) Joseph ScaliseHouse GOP slated to unveil agenda ahead of election House panel details 'serious' concerns around Florida, Georgia, Texas, Wisconsin elections Scalise hit with ethics complaint over doctored Barkan video MORE (R-La.) have both come out in support of that idea.

Meanwhile, some Senate Republicans have sought to rein Trump in.

Sen. Lindsey Graham Lindsey Olin GrahamMcConnell locks down key GOP votes in Supreme Court fight Will Republicans' rank hypocrisy hinder their rush to replace Ginsburg? Momentum growing among Republicans for Supreme Court vote before Election Day MORE (R-S.C.) told CNN’s “State of the Union” on Sunday that any effort to oust Mueller would be “the beginning of the end” of the Trump presidency.

Some Republicans who spoke to The Hill shared that assessment.

“There is no appetite among the Republican establishment to remove Mueller,” one GOP operative warned. “If the president fires him, he could be impeached."

The Memo is a reported column by Niall Stanage, primarily focused on Donald Trump’s presidency.