If Rosenstein were, in fact, fired by the White House or resigned, he would no longer serve as the acting attorney general for purposes of the Russia investigation led by Special Counsel Robert Mueller. The succession issues surrounding his potential departure are crucial to the continued viability of these all-important inquiries.
As Marty Lederman noted, without action, most of Rosenstein’s deputy attorney general (DAG) responsibilities would automatically have passed to the Principal Assistant Deputy Attorney General (PADAG) Edward O’Callaghan. Therefore, if the White turns to Matthew Whitaker, Attorney General Jeff Sessions’ chief of staff, it would represent an affirmative and remarkable choice to elevate Whitaker, and not O’Callaghan.
However, those machinations are a separate matter from who would assume responsibility to oversee the Russia or “hush money” investigation involving President Donald Trump’s former personal attorney, Michael Cohen. Mueller reports to the attorney general, and Rosenstein was serving as the acting attorney general for those purposes, because Sessions had to recuse himself. The same is true for the hush money investigation being conducted in the Southern District of New York. There, the acting U.S. attorney (because the U.S. Attorney is recused due to his involvement in the Trump campaign) presumably reports to Rosenstein in his acting attorney general role as well.
So what happens to the oversight of those investigations if Rosenstein departs?
As Steve Vladeck notes, the Vacancies Reform Act allows Trump to appoint an acting deputy attorney general, but such an appointment does not automatically become acting attorney general for purposes of Russia or hush money investigation oversight. Consistent with Steve’s understanding, the New York Times reports that Solicitor General Noel Francisco would oversee the Mueller investigation while Whitaker takes over as Deputy Attorney General.
One caveat: The reason why the new acting Deputy Attorney Genera can’t oversee the Russia and hush money investigations is due to a rule that an “acting” Justice Department official cannot perform “acting” functions of another official. There is some debate on whether this rule is a settled matter, as Kel McClanahan explains:
This is correct. Sort of.
So here's the thing. The "no double acting" is a DOJ PRACTICE, but I don't think it's actually a law or reg anywhere. It's a norm. And we all know how Trump feels about following norms.
I'm not making a joke here. To his credit, most of the "rules" …
— National Security Counselors (@NatlSecCnslrs) September 24, 2018
At the same time, some have raised questions about whether Francisco might need to recuse himself from oversight of the Russia investigation because Jones Day, Francisco’s former law firm, represented the Trump campaign. As Lederman noted, as solicitor general, Francisco has been recused from all Supreme Court cases in which Jones Day has represented a party. But unless and until that recusal happens, Francisco will be the acting attorney general for purposes of overseeing the Russia and hush money investigations. If Francisco were recused, the baton would presumably be handed to the next in succession, which would be the current Assistant Attorney General for the Office of Legal Counsel Steve Engel.