Washington – Allies of President Donald Trump are campaigning for him to fire the man who oversees special counsel Robert Mueller's investigation into Russian meddling in the 2016 election, but such a move could get messy — and even provoke a legal challenge.

Some House Republicans have been fuming at Deputy Attorney General Rod Rosenstein for being slow to respond to congressional requests for documents related to other matters. And Trump has been angry at the FBI for raiding the office and home of his longtime attorney, Michael Cohen — a move approved by Rosenstein.

But removing Rosenstein — and putting someone else in charge of the Mueller probe — may not be quite as easy as it sounds.

Under normal circumstances, firing Rosenstein would trigger the Justice Department's line of succession plan and two things would happen.

First, one of Rosenstein's top assistants would become acting deputy attorney general for everything but the Mueller investigation.

Then, Solicitor General Noel Francisco would be in line to head up the Mueller probe.

But Francisco might have a conflict of interest, raising the possibility of a recusal, said Victoria Bassetti, a fellow at the Brennan Center for Justice at the New York University School of Law. That's because his former law firm, Jones Day, did legal work for the Trump campaign.

If Francisco recuses himself, the next in line would be Steven Engel, who heads the Justice Department's Office of Legal Counsel. Engel, however, worked on Trump's transition team and also might face a conflict of interest.

Then the duty would fall to John Demers, who heads the department's national security division.

"Decisions about the special counsel would be then made by someone else already at the department, and there is no predicting how they would act," Bassetti said.

If Trump fired Attorney General Jeff Sessions — who has recused himself from overseeing the Russia investigation — he could pick an acting attorney general to oversee Mueller regardless of whether Rosenstein is fired. Under the 1998 Vacancies Reform Act, Trump could pick anyone from within the administration who has already been confirmed by the Senate or someone in the career leadership ranks within the Justice Department.

But there's a legal debate about whether the vacancies act can be used to replace someone who was fired, meaning actions taken by that official might be challenged in court, Bassetti said.

On the flip side, the Justice Department's Office of Legal Counsel issued a legal memo in November stating that the 1998 act can be used to replace someone who was fired. Bassetti said the office's interpretation is also open to legal challenge.