I don't think that the United States can call itself and/or hold on to the belief that it is an exceptional state.
Perhpas in the past, e.g: The Cold War Era, it can be considered an exceptional nation, due to the fact that it was not just economically, but militarily strong as well. The individual freedoms that American citizens have over their Eastern Bloc counterparts had, also helps to perpetuate the belief in others that the United States was an exceptional nation.
But in recent years China, India and other countries of the world are also becoming economically and militarily strong as well. Not only that, these countries are taking an active role in influencing world politics, whereas the United States is taking a more passive role in influencing world politics.
The 1st Gulf War was justified by the Iraqi invasion of Kuwait. But the 2nd Gulf War was not justified at all. The attack on Iraq, based on the belief that it had WMDs has not been substantiated, and thus the deposing of Iraqi Dictator, Saddam Hussein, should not be legal at all. It is the same as the Iraqis attacking Kuwait. I the United States would attack another sovereign nation without cause, then surely that doesnot speak much for American Justice, and the system that the rest of the world should aim to follow.
In effect, I do not think that the United States is an exceptional nation any longer. The time has come where the United States should see itself as equals on the world stage, with no authority to impose itself on other nations, as it would have itseld believe. In fact, no nation should think themself exceptional to other nations, as this would give them unrighteous cause to impose their views on other nations, and that would be a severe blow to World Unity and World Peace.