I think at the end of the day, the president knows they benefit in the long run from enforcing federal supremacy over the states, so if the dispute involves a state law, they will still enforce the court's decision on the state, if perhaps half-heartedly.
The more interesting case is if SCOTUS strikes down a federal law, say the incumbent president's major legislative accomplishment from a year or two earlier, and then the president (backed by at least 34 senators) says "You and what army?" and continues to enforce the law held unconstitutional (perhaps against everyone but those specific plaintiffs in that specific case*). I think the obvious answer is the law remains in effect until the next election, with the president's opponent running on enforcing the SCOTUS decision if they win. In a particularly severe case, this could start a secession crisis or even a 2nd civil war if a portion of the military rebels. It's unlikely, but this is a road we definitely don't want to go down as a society.
*My understanding is this how Lincoln pushed back against Dred Scott.
Even that is a two-way street in this age where every major politician is much more dependent on their base than they were even in the Bush years. Why would you enforce something that harms your base when then the base then won't show up next year because you betrayed them? They aren't going to change sides, but they might stay home. Just ask Governor McAuliffe about that. But yes. I will agree that a president continuing the enforcement of their unconstitutional law would be a bigger crisis than even the thing I described.
When people talk about a new Civil War, I can't stop thinking about what else could happen besides the United States at least temporarily dissolving.
