Jim Evans has an interesting essay at Ethics Daily that talks about what a "Christian Nation" would be doing. Here's his conclusion:
If we are serious about this Christian nation stuff we might want to re-visit our attitudes and practices towards the poor. As Jesus himself noted, it is not how energetic we are in shouting his name that matters, but rather how faithfully we attend to the matters he taught were really important. Otherwise, it may be that we really don't know him.
While I agree with Jim about the need to do more for the poor, I'm still uncomfortable with all talk about "Christian Nations." As I see it, talk about a "Christian Nation" is oxymoronic. By definition, all nations act out of "self-interest." They are incapable of putting the interest of others above their own. The best they can do is strive for actions that are in "mutual self-interest" with other nations.
Christians live by a completely different standard. The love God has shown us through his Son removes the necessity to act out of self-interest alone and enables us to put the interests of others above our own. Christians are empowered to act "self-sacrificially." That is something that nations, as we have defined them, can never do.