Does the president have a duty to defend every law? | Lyle Denniston at Constitution Check

Lyle Denniston at Constitution Check: Article II, defining the “executive power” of the national government, says that the president “shall take care that the laws be faithfully executed.” But the Constitution itself is obviously one of the laws undoubtedly within the president’s care, and the presidential oath makes that a binding duty. What does the occupant of that office do if legal advisers claim that a law passed by Congress is unconstitutional? Does it still get “faithfully” enforced?