Personally, I think it's stupid to apply a religious affiliation with any political body. Applying such labels to political entities, in my opinion, simply destroys the credibility of said religion because there is no way a political entity can espouse the virtues of that religion.
In the case of Beff's question, I suppose one must ask:
What is America and what is Christianity?
Does being founded by a bunch of guys who believed themselves to be Christian automatically make America "Christian" by default? Does having a President who believes themselves to be Christian automatically make America "Christian" by default?
If so, then if America has a President of another religion, then the 'religious' identity of the country would then change.
Most religions are typically mutually exclusive which, of course, conflicts with the principals on which America was founded, at least, as I understand them (all men created equal, land of opportunity, haven for the free, religious tolerance...etc..etc..).
I believe that religion is a person's personal choice and if they make such a choice and claim fealty to a certain god or set of principles that is all well and good. What I see, however, is instead of people using their personal choice as an opportunity to mold their own lives according their principles of preference, they mistaken their "personal choice" as a charge to force others to make the same choice they did (as if these 'unbelievers' will give their own choice some validity).
Even more, though, I believe that if a person chooses to run for public office (in USA), they are no longer claiming fealty to a certain god or set of principals but to the people they want to lead/represent. If you want to work towards a position of leadership in a society that defends people's right to choose their own paths, that means defending those opportunities you would not choose for yourself for those who have the right to make those choices.
If your conscience will not allow you to do that, then you have no business running for public office.
Does that happen? No.
The leaders who consider themselves Christian not only want the cake they want to eat it as well. Not at all Christian in nature but then again, those christians who fled religious persecution were fleeing other christians and ended up persecuting the native americans and burning wiccans at the stake.
Go figure.