1. Congress enacts laws for whatever reasons it will. Members of Congress may have stirring debates about the constitutionality of a particular law, but in the end Congress will do what it will do. It's true that Congress should enact only constitutional laws, but that's like saying children who live in a match factory shouldn't play with matches.
2. If the executive doesn't like a particular law for any reason (one of which may be his opinion that the law is unconstitutional) he may veto the law. If his veto is overridden, the law is the law.
3. In the absence of a specific judicial decision nullifying a specific law, the executive is bound to enforce that law. That is what the Constitution contemplates: The legislature legislates and the executive executes. There's nothing mysterious or arcane about that.
4. If a party with standing challenges a law, it's up to the courts to decide whether or not it's a constitutional law. As it says in Article III, Section 2, of the Constitution:
The judicial Power shall extend to all Cases, in Law and Equity, arising under this Constitution, the Laws of the United States....Which means, as far as I'm concerned, that the executive must defer to judicial decisions about the application of a specific law.
That should do it. Why make it needlessly complicated when we have the structure and words of the Constitution to guide us?