I would be somewhat surprised if the Congress ended up doing it, but seeing how spineless they already are wrt Trump even where he contradicts them, not super surprised.
My point, rather, is that, should such a thing happen, it would be a bona fide constitutional crisis. If two branches of government are openly in defiance of parts of the Constitution, it becomes a free for everyone else, as well. Secession would suddenly be on the table for real - after all, the Constitution is what makes the Union, so if the Constitution is no longer the supreme law of the land, then the states could reasonably argue that they aren't bound to the Union in any sensible way. Or they could simply state that per the Emoluments Clause, they consider the president illegitimate from there on, and so no EO and no act of Congress signed by him has force of law on their territory. Or even invoke the 9th and the 10th Amendments in a full-on literalist vein (stealing the book from fringe factions of the right), and just claim that the feds simply don't have most powers that they claim as well.
This is all very far-fetched, but in the event of an open defiance of SCOTUS by the other two branches, we'd already be in the realm of far-fetched things, so the impossible becomes possible, and unlikely becomes probable.
http://www.vox.com/policy-and-politics/2017/1/24/14358654/tr...
The interesting thing about this is that it's a bipartisan affair as far as party affiliations go: the two main guys behind it are the ethics people for Bush and Obama, respectively.