Marbury v Madison never reneged on whether Marbury was entitled to the commission, Marshall simply noted that even though the law was on Marbury’s side, the actual law that gave the Supreme Court original jurisdiction on matters such as that was unconstitutional. As the constitution only allows Congress to alter the appellate jurisdiction of the Supreme Court, the narrow original jurisdiction of the SCOTUS cannot be curtailed or expanded by Congress, and only by expanding it was this case part of the SCOTUS original jurisdiction. Marshall essentially said “all matters of law favor Marbury, and there is a valid remedy–except, since this is a case filed directly with the SCOTUS, and in an area where the SCOTUS cannot constitutionally have original jurisdiction, it’s unconstitutional for us to do anything needed to redress the wrongs. Instead, we can simply note this case, constitutionally, does not belong in this court as a directly filed matter, the law that expands this court’s original jurisdiction is unconstitutional and void.”
I suppose in theory Marbury could have refiled with a lower court and appealed his case up to the SCOTUS and maybe Madison would have been issued a writ of mandamus requiring deliverance of Marbury’s commission. But he never did that, I don’t know the history of why or why not.
But unlike many court rulings, Marshall decided to establish precedent on issues that he did not need to in order to issue his ruling in Marbury, and some of that precedent is relevant to this case. Specifically, that yes, the executive branch has no discretion in executing ministerial functions and that yes, in general the judicial branch can issue writs mandating execution of those ministerial functions. Obviously the most important aspect of Marbury is when Marshall declared a law passed by Congress to be unconstitutional, which established judicial review (it was not explicitly established by the constitution.)
[As with all judicial branch rulings, just like Nixon could have ignored the order to turn over his tapes or etc the executive branch could likewise ignore the writ, but it would make it without doubt that the executive was behaving illegally at that point. Politically it’s far different to just ignore a court order than it is to engage in “creative” interpretation of the laws.]
Except we have a Supreme Court ruling that obliges executive officers to perform their ministerial functions. Marbury was v Madison because Madison was the minister who was not performing his duty. It’s questionable if the President has such ministerial functions (and thus a suit would probably most appropriately be directed against the DHHS Secretary IMO.)
The rule of law essentially will collapse if the President can decide which laws the legislature passes that he cares to enforce and nothing is done about it. What would stop the President from agreeing to “bargains” in which there are tax increases but some spending cuts, and then he just says “no, we’re going to keep spending whatever we want but I’m keeping the tax increases, too.”
When it’s an issue of declining to execute purely ministerial functions, for sure.