I have watched all of Deputy Attorney General Rod Rosenstein’s public statements. My take based on this and reporting about what he sees his role to be here is that this is a guy who wants his legacy in history to be that he stood between Donald Trump and a constitutional crisis.
I will make a prediction, with a high degree of certainty, that Rosenstein won’t resign.
I also feel fairly certain that Trump will not fire him on Thursday or before the midterms. This would stir up democratic turnout and further endanger the Senate. Also, he knows a lot and would be free to talk to the media and write a book. A demotion serves their purpose. There are ways to neutralize him that don’t require a dismissal from the DOJ. Trump’ doesn’t need to endure the backlash from a firing based on a report published in what Trump calls “the fake NY Times”.
The most likely scenario is that Trump will dismiss Attorney General Jeff Sessions after the midterms or allow him to resign and then make a decision about Rosenstein. If he can coerce a resignation from Sessions, Trump will have the option of a AG appointment through the Vacancy Act. At that point, the new acting Attorney General would directly oversee the Muller investigation. Rosenstein would probably be replaced as deputy and moved elsewhere within the department.
Trump’s has different procedural options should he choose to fire Sessions. He would need to get a new AG through a confirmation process unless he tried a recess appointment which is not likely as that would create a political firestorm from all sides however.
Trump’s obsession with the removal of Sessions seems to be a priority over taking on Rosenstein and lighting that fuse. Rosenstein won’t be overseeing the Muller investigation at some point but not because he resigned or was fired.