Mr. Mueller was appointed not by Mr. Trump, but by Deputy Attorney General Rod Rosenstein after Attorney General Jeff Sessions recused himself from involvement in any investigation related to the 2016 presidential race. That means Mr. Trump couldn’t fire Mr. Mueller himself, but would have to order Mr. Rosenstein to do so.
Mr. Rosenstein has expressed support for Mr. Mueller, and his associates expect him to resign rather than carry out such an order. If that happens, Mr. Trump could turn to the next Justice Department official in line, acting Associate Attorney General Jesse Panuccio, and then to Solicitor General Noel Francisco.
It isn’t known if either would heed an order to fire Mr. Mueller. If they refuse, Mr. Trump would have to go down the hierarchy at the Justice Department until he found an official willing to do so. In such a situation, the president could face a number of DOJ resignations—and the political fallout that would entail.
Something like this happened on Oct. 20, 1973, when President Richard Nixon ordered Justice Department officials to fire Watergate special prosecutor Archibald Cox. Attorney General Elliot Richardson resigned, as did his deputy, William Ruckelshaus. Solicitor General Robert Bork finally did as Mr. Nixon asked. That episode became known as the Saturday Night Massacre.
.. Some legal experts have asked whether Mr. Trump might replace Mr. Sessions or Mr. Rosenstein with another official and order that person to fire Mr. Mueller.
Attorneys general and their deputies must be confirmed by the Senate. Someone who is temporarily “acting” in that position, without Senate confirmation, must come from an existing Justice Department job or a Senate-confirmed post elsewhere in the administration.