1. A US court orders something.
2. The Executive Branch enforces that order, as it is responsible for the DOJ which is in turn responsible for the US Marshals (who enforce court rulings).
3. If those people do not enforce the rulings, Congress brings articles of impeachment and impeaches the President or others responsible.
4. Elect/appoint/elevate a new person to carry out the court order.
The Constitution doesn't really account for the possibility that 1/3 of the Senate would disagree with an ignored court order. So hard to say where it goes from there.
Conversely, presumably this is by design since a rogue judge could issue a bad court order and presumably there are mechanisms to deal with these that perhaps involve a large enough quorum disagreeing with and ignoring it.
The constitution is premised on leaders respecting laws and norms.
Supposedly at that stage everyone would stop following their instructions. This may be part of why Trump is so set on replacing huge swaths of the government with loyalists.
Keep in mind that people like the US Marshals and federal agents get guidance from the President all the time. Think "we won't arrest anyone for federal drug laws in states where recreational marijuana is legal."
The difference seems large enough that you could conceivably respond differently to one versus the other.