Congress would most likely rely on the following:
The Supremacy Clause of the United States Constitution declares the laws of the Constitution as supreme over state laws. In the case of conflict, federal law takes precedence over state laws and state constitutions. This cqn be found in Article 6, Clause 2 of the United States Constitution.
States would most likely rely on:
The nullification theory allowing states to nullify federal laws they find as unconstitutional, or interposition the right of a state to interpose between the states citizens and the federal government.
