Someone posed a question to me over the weekend that may soon be relevant. In fact it seems inevitable that it will be relevant given the current president's shall-we-say rather unilateral conception of his legal authority. What happens when the Federal courts issue an order and the Executive branch simply ignores it?
It has been some time since I've taught Presidency, so I'm rusty on Andrew Jackson and Worcester v Georgia (the source of the infamous misquote, "John Marshall has made his decision; now let him enforce it!" He actually said the more mundane but identical in spirit, "the decision of the Supreme Court has fell still born, and they find that they cannot coerce Georgia to yield to its mandate.") With that caveat…
First, failing to execute a Court order would be as clear cut as grounds for impeachment could get. Since Article II requires the Executive to "take care that the laws are faithfully executed," failure to do so would be an open and shut case. Impeachment is not an automatic process, of course. So it is conceivable that the House GOP would not make an indictment even if the situation demanded one. That's where things get more complicated.
A Federal Court has the power to issue an arrest warrant through its quasi-enforcement branch, the United States Marshall Service. While issuing such a warrant for the President would be unprecedented and frankly sensational, the holder of that office is not above the law. I imagine that a president would have to push a court pretty far before it came to this, but it is not impossible. The President failing to follow a court order is not quite the same as the court issuing a warrant for someone who violated a statute, obviously, so there would no doubt be a lot of parsing of technicalities involved. Another (less likely) option is the Justice Dept., which resides in the Executive branch, bringing criminal charges of some sort against the president. There would be attempts to block this from the top, but one has to imagine that someone in the Department seeks glory and attention enough to run the risk of trying it and hoping to god that it works.
This would qualify as a clear example of the overused term "constitutional crisis." The functioning of our system depends on the very basic division of powers and responsibilities upon which the Federal government is built. Sadly, and without lapsing into undue alarmism, it appears that the current president is of a mindset to refuse to take orders from anyone other than himself.
Or the Kremlin, obvi. He takes plenty of orders from them.