IMO the courts have more to say than the Constitution.. it seems at times.
My reading of the Constitution and a little history is that the term "United States" was in fact the united states. Each state was a State. I do not think that the Constitution had the intention of anything else. However since the Civil War I believe the United States has become an entity and the states are mere parts. Can't blame that on Article I Section 8. Blame the likes of the Warren Court. :)
Each state was a state and each state is a state. And each county is a county.
The United States was a consolidated government created by "We the people of the United States." By adopting the Constitution, the people of this country created political bonds with one another. Those bonds cannot be cast aside by any state or county or city. These lesser entities cannot cancel my status as a citizen of the United States and these lesser entities cannot sever my political bonds with Americans living in other states or counties or cities.