Mr. Dowd, like any reasonably sentient person, knows there is no way that a conversation with Mr. Mueller would go well for the president. Mr. Trump doesn’t have a relationship to the truth, but may at one point have had a fleeting affair with it, albeit one apparently covered by a nondisclosure agreement. He lies with pleasure and abandon, then brags about it later. Yet on Thursday, Mr. Trump, who has built his career on the belief that he can brazen his way through anything, told reporters that he “would like to” testify.

At least when Mr. Dowd climbs into bed tonight, he can rest easy, knowing that he did all he possibly could for an impossible client. His last significant public comment as Mr. Trump’s lawyer was to call on the Justice Department to shut down the Russia investigation — a position he attributed to Mr. Trump before backtracking and claiming it as his own.

The president’s legal team appears to be falling apart just as his legal problems are mounting, both from the Russia investigation and, more recently, from women who say they’ve had affairs with Mr. Trump and are seeking to be released from agreements to silence them. Before Mr. Dowd’s departure, Mr. Trump had spoken to associates about firing Ty Cobb, the White House lawyer who has been advocating a cooperative approach toward Mr. Mueller. Meanwhile Mr. Trump has reached out to, and been rebuffed by, at least two legal heavyweights in the last few weeks: Emmet Flood, who represented President Bill Clinton during his impeachment process, and the conservative superstar Ted Olson.

In their stead the president has brought on Joseph diGenova, a lawyer who has argued on television that the Justice Department and the F.B.I. are framing Mr. Trump. Who else is there? Alan Dershowitz, the celebrity defense lawyer and self-described liberal from Harvard who has taken on the unlikely role of Trump defender? Or Marc Kasowitz, who previously represented Mr. Trump before leaving because he, among other things, threatened a stranger over email?

The bigger problem for Mr. Trump is that there aren’t many experienced lawyers who will want to take on a client like him — save, perhaps, Michael Cohen, a longtime loyalist and Trump lawyer who may be in serious legal trouble of his own, and Roy Cohn, who is dead. Mr. Cohn, a litigious thug who helped destroy the lives of many decent people before being disbarred for “particularly reprehensible” ethical violations, took a young Mr. Trump under his wing and taught him how to use the law: as a concealed weapon, brandished primarily in the service of vengeance or survival. Mr. Trump was an avid student, as evidenced by the empty threats of litigation he aims regularly at reporters or the unconscionable nondisclosure agreements he wrests from his paramours and underlings.