What could that excuse look like?

While it is difficult to project arguments that might be advanced by the world's most powerful paranoid old man, he could have Rosenstein try to portray, say, former FBI deputy director Andrew McCabe's wife's connections to former Virginia governor and longtime Clinton ally Terry McAuliffe—another favorite subject of recent presidential tweets—as evidence of some sort of conflict of interest. I don't know how he'd tie this to Mueller, exactly, but the existence of gaping plot holes has never been a major obstacle to this president's willingness to tell stories.

Trump has also suggested that the special counsel would cross a "red line" if he were to start poking around the family finances. Since reports indicate that this is exactly what Mueller has been doing of late, perhaps the president might try painting that as the type of "misconduct" that merits termination.

This is not a space in which any old excuse will do, though. The first approach, as explained in a recent Citizens for Responsibility and Ethics in Washington paper, risks inviting a lawsuit on Fifth Amendment grounds, particularly if Mueller's termination were justified by false statements that impugn his character. The problem with the second approach is that Rosenstein's order that appointed Mueller empowers him to look not only at potential collusion, but also at "any matters that arose or may arise directly from the investigation." If his work yields no signs of collusion but does turn up evidence of—and this purely a hypothetical—massive financial fraud, following up is very much within the scope of what he can do. It would be tough for Rosenstein to recast as "misconduct" something he authorized without looking like a giant stooge in the process.

What if Trump doesn't want to bother with "legal obligations"? What if he just orders Rosenstein to do it?

A fair question, given the president's previously-professed views on the ability of the justice system to limit what he can do. As argued by former solicitor general Seth Waxman, if Mueller is terminated without any explanation, he (or his subordinates) might try suing under the Administrative Procedures Act, which allows courts to prevent agencies (like DOJ) from taking action (like removing the special counsel) that is, among other things, "arbitrary, capricious, an abuse of discretion, or otherwise not in accordance with law." Since the law delineates the circumstances in which Mueller can be removed, Waxman argues, it affords a remedy in the event that those rules are broken, too.

Wouldn't this stuff take forever?

This is a federal courthouse we're talking about, so yes. But before any of Mueller's hypothetical cases could get underway, he would likely seek a preliminary injunction that prevents his firing from taking effect until the court can decide the matter on the merits. Judges evaluate requests for injunctive relief on a case-by-case basis, but among the many factors they consider is whether granting the injunction would serve the public interest—a prong on which one would assume Mueller could make a particularly strong argument in this instance.

If he wins, then for as long Mueller's attorneys and the Department of Justice battle one another over the intricacies of Administrative Procedure Act and the legitimacy of his termination, he would remain on the job, free to carry out his work as usual until the court says otherwise.

Would Mueller have any recourse outside the court system?

In theory, yes. He could plead his case to Paul Ryan, who would be understandably horrified that the President of the United States had so flagrantly attempted to undermine the rule of law in this country. Ryan and his fellow legislators could take action to reinstate Mueller and/or to enact more stringent limits on the ability of administration officials to remove him from office in the future, and could draft articles of impeachment on obstruction of justice grounds, at the very least.