Well, this is going to go in the direction of political theory...
The United States was originally just that, independant states that agreed to honor a limited set of principles listed in the Constitution, but the Civil War changed that.
Now, whatever the Fed says goes. So, to answer your question, we are supposed to have a sovereign state and a seperate, sovereign (but limited) Fed. This means that if one is accused of murder (a state crime) then the state and only the state can try you. But since we are now post-Civil War, you can be tried again on a whole bunch of made up Federal crimes (crimes in which you do not have to cross state lines to commit). Witness the lady from Washington who grows pot - no state lines are crossed and her state (Washington) says it is legal. The Fed comes in and charges her anyways.
Now, I realize that this particular example is not double jeopardy; it is over stepping jurisdiction, but it does prove my point - today, for better or worse, we have Federal supremacy.
On some level however, this issue of "how many sovereigns" is a moot one. The Constitution is clear - no second trial of the same crime. Every state has agreed to this when they were accepted into the Union. The Constitution does not quibble over Fed or state (or county or municipality for that matter). To say, "We can try someone twice because a different governing body is doing it" is equivalent to saying that "We can outlaw Judeaism in Denver because the Denver city council has jurisdiction within Denver".
Soon we will have Freedom of Speech but it will be a Federal crime to open your mouth...or a civil offense of "unlawful mouth opening".