The problem with this Republican critique is that Obama has always affirmed that the U.S. is exceptional; such a view isn't incompatible with the belief that many if not all countries are exceptional. This explanation won't satisfy Americans who really want affirmations of American supremacy, but they have less to complain about after the President's speech on the Syrian crisis. Obama invoked exceptionalism in the final paragraph of the speech, and it's the exceptionalism of American entitlement, the assertion of an exceptional prerogative, regardless of the preliminary disclaimer.
America is not the world’s policeman. Terrible things happen across the globe, and it is beyond our means to right every wrong. But when, with modest effort and risk, we can stop children from being gassed to death, and thereby make our own children safer over the long run, I believe we should act. That’s what makes America different. That’s what makes us exceptional. With humility, but with resolve, let us never lose sight of that essential truth.
What makes America different? What makes America exceptional? As far as I can tell from this paragraph, it is that we can do something, and so we have a right to do it. Policing the entire globe effectively may be beyond our means, but the aspiration to do so is not beyond our rights. If humility comes into it, it's a matter of knowing the limits of our ability, not the limits of our prerogative.
Such an assertion of exceptionalism may still not satisfy jingoists who want plain assertions of American moral superiority, but it's bad enough as it is. Some Americans want to believe that our values make us exceptional, but Obama seems to be saying that our power makes us so. This is the exceptionalism of the Clintons and Madeline Albright, the people who asked why the U.S. had such a massive military if we weren't going to use it, and answered the question by using it. Restating this has earned Obama praise from one quarter. This is Richard Cohen of the Washington Post, who still thinks Obama is doing too little, too late:
The phrase “American Exceptionalism” is often a demagogic expedient. It suggests that America is particularly beloved by God –more so than any other nation. It is poppycock, rhetorical cocaine for conservatives. But tonight Obama employed it in a sensible way: America is exceptional because we have the wherewith all to stop the killing and deal harshly with the killer.
If the results are the same without resort to "rhetorical cocaine," then Cohen's is the proverbial distinction without a difference.