https://www.politico.com/magazine/story/2017/08/03/could-trump-fire-mueller-its-complicated-215453
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Can Trump fire Special Counsel Robert Mueller directly?
Probably not, although
some disagree.
So who can? Department of Justice regulations make clear that Mueller may be fired by the attorney general only for “
good cause.” Deputy Attorney General Rod Rosenstein, who serves as the acting attorney general for Mueller-related issues due to Jeff Sessions’ recusal, has made clear in congressional testimony that he’s seen
nothing of the sort.
If Sessions is replaced as attorney general, then his successor would not be recused, and could either gin up good cause to fire Mueller or (more likely) rescind the good-cause requirement and then terminate him.
Various senators have publicly warned Trump not to fire Sessions, which suggests that if he’s inclined to do so, he’d prefer a method that lets him sidestep the Senate.
If Trump fires Sessions, can he install a replacement without going through the Senate confirmation process?
Almost definitely.
While many (
including me) have fretted about the possibility of a recess appointment, that door is likely to shut, even though the Senate is expected to break on Thursday for its August vacation. Under the Constitution, “The President shall have Power to fill up all Vacancies that may happen during the Recess of the Senate, by granting Commissions which shall expire at the End of their next Session.” In other words, if the Senate skips town, he doesn’t need their vote, and the new person would serve until the end of the next congressional session, i.e. the end of 2018.
In recent years, however, the Senate has tried to clamp down on attempts to sidestep its authority through recess appointments. Starting in 2007, the Senate began convening “pro forma sessions” during what would otherwise be a recess. No actual work transpired at these sessions, just a quick gavel-in and gavel-out. President Barack Obama tried to call the Senate’s bluff by making recess appointments during these times, on the theory that a recess interspersed with
meaningless kabuki is still a recess. The Supreme Court disagreed, and
invalidated those recess appointments in 2014. The court held that it’s for the Senate to decide what is and isn’t a recess, and that even if it walks and talks like a duck, the Senate can still call it a chicken.
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Of course the left would be really angry and he'd get bad press.