It was unclear whether or not Rosenstein, who oversees major parts of the Justice Department, including the special counsel's Russia probe, would keep his job. Amid conflicting press reports Monday, the White House said Rosenstein will remain in his job for the time being, and he will meet with the president one-on-one on Thursday.
If Rosenstein were to depart, it was also unclear whether he would be fired, or he would resign. In Rosenstein's case, this could make a big difference as to whom Trump can select to replace him as deputy attorney general.
The question of who would oversee the Russia probe is slightly different, however, because Rosenstein has been effectively wearing two hats since Attorney General Jeff Sessions recused himself last year from any role overseeing Robert Mueller's investigation. One hat is that of deputy attorney general. The other is that of acting attorney general for the Russia probe, because Rosenstein was acting as a stand-in for Sessions.
Any replacement of Rosenstein by Trump, therefore, would be a replacement of his deputy attorney general position, not a replacement of the other role, acting attorney general for the Russia probe. That responsibility would go to Solicitor General Noel Francisco, and experts agree that the law gives Trump little control over that aspect of the succession.
Still, the question of how much control Trump would have in who replaces Rosenstein could have far-reaching implications. A Rosenstein replacement could take steps to protect the president from investigation, to seal records, withhold funding from Mueller, and otherwise slow the work of the special counsel to a crawl.
With that in mind, here's why the "fired" vs. "resigned" question could be very important.
The replacement of government appointees is largely governed by the rules set forth in the 1998 Federal Vacancies Reform Act. This law gives the president the authority to temporarily move any one of his Senate-confirmed political appointees into a position that is vacant, provided the person who leaves the positions "dies, resigns, or is otherwise unable to perform the functions and duties of the office."
The law specifically does not say "dies, resigns or is fired."
In the case of firings, the federal government has a succession plan, under which temporarily vacant posts are typically filled by a deputy to the person who departs, or by another person who has been confirmed by the Senate within that department. This is in part to make sure that continuity is maintained in agencies with tens of thousands of employees and billion dollar budgets.
But it is also in place, experts say, to preserve the Senate's role in the confirmation process and to make sure the president can't simply bypass the Senate and fire someone in order to put whomever he or she wants into that position, even if that person has not been confirmed to work in that particular agency.
Trump, however, has challenged this long-held practice. When Veterans Affairs Secretary David Shulkin was ousted earlier this year, Trump quickly named Robert Wilkie, undersecretary for personnel and readiness at the Defense Department, to temporarily fill Shulkin's position.
But according to a lawsuit filed against the Trump administration by veterans advocacy groups in April, Trump broke the law by disregarding the order of succession at the Veterans Affairs Department and installing Wilkie, who is not related to this reporter, atop the agency.
The plaintiffs in the case argue that because Shulkin did not resign, or die, or become ill — he says he was fired — Trump did not have the authority to choose whomever he wanted to temporarily fill Shulkin's spot. According to the succession plan of the VA, they argue, Trump was required to name Thomas Bowman, deputy secretary of the VA, as acting secretary until another VA secretary could be fully confirmed by the Senate.
In Rosenstein's case, the stakes are much higher, given that Sessions has recused himself from the Russia probe. Trump has effectively gone to war against his own Justice Department, primarily over the Russia probe, which is run by former FBI director Robert Mueller, but also for what the president sees as a failure by the department to pursue his political enemies.
If Rosenstein were to resign, then the Vacancies Act would give Trump broad leeway in appointing Rosenstein's temporary successor, and some fear the president would install a political ally willing to cripple the Mueller probe.
If, however, Rosenstein is fired, then the argument that Trump must follow the federal order of succession becomes significantly stronger.