If Congress passes a law saying that the president is required on every Saturday to get up and flap his wings and fly around the room, what do you think he should do with that?

Obviously he should ignore that law because it is ridiculous.

Yes, the Executive is free to ignore unconstitutional or ridiculous laws. And it doesn't take anything involving courts to resolve that dispute.

Keep in mind that Congress is free to pass a law saying that the President must flap his wings and fly around the room, and then impeach any president who does not follow through with that.

The courts are not involved in that dispute. It is between those two branches.

And it's up to voters as to whether we want to elect congresspeople who will impeach presidents without the ability for flight.

Yeah, I'm being a little ridiculous with this example, but it does illustrate the design and function of the US government.

Congress authorizes spending, but it is up to the executive branch to execute what it wants to, and then it is also up to Congress to impeach over basically anything if they don't like what the president does.