Exactly. The budget itself is a law that the executive is required to carry out. If Congress passes contradictory laws, the president has to make a decision on which to obey, and is supposed to do whatever gives him the least arbitrary power. Just following the budget is less arbitrary than effectively wielding a line-item veto by deciding which items get funded.

Then the economy will carry on, and if the GOP sues and actually wins, it will be very clear that they were the ones who blew it up. I doubt they'd be dumb enough to carry through with that.