While rereading the entire thread I came across a valid counterargument put forth by Burn: the ICC is a violation of the US constitution.
Is this true? This is what I found:
COSSACK: Ambassador Scheffer, in hearing that, that's totally different than the traditional American system that we have here with a jury. And do you think that that would create special problems for people to sign -- for the United States to sign on to something like that? To give up the traditional trial by jury?
SCHEFFER: No, when we were negotiating the Rome treaty, we always kept very close tabs on does this meet U.S. constitutional tests, the formation of this court and the due process rights that are accorded defendants. And we were very confident at the end of Rome that those due process rights, in fact, are protected, and that this treaty does meet a constitutional test.
So, keep in mind that most of the world, in fact, does not have a jury system and does not render criminal justice the way we do in the United States or in the United Kingdom or other common law countries. Most of the world prosecutes criminal defendants in accordance with civil law concepts, where judges not juries are in fact the determiners of the final judgment.
So we know that. We weren't surprised by it, and we were able to work very comfortably with that. But we had to keep our eye on the ball of what are the due process rights that are being protected in the statute? And, in fact, we're doing that now in further negotiations for the rules of criminal procedure and evidence for the court. We're deeply engaged in making sure that those rights, in fact, can be preserved.
http://transcripts.cnn.com/TRANSCRIPTS/0001/02/bp.00.html
David Scheffer led the US delegation to the Rome Conference (10 years ago, here it is James), but still voted against treaty.
Constitutional issues, apparently, didn't play a role.