I believe the answer is yes in three important ways.
1) Many, but not all, of the principles which informed our constitution came from devout Christians or even nominal Christians in a very Christian culture. I am not of the opinion that someone like Thomas Jefferson was undeniably Christian, but it does seem undeniable to me that all the founding fathers were immersed in a Christian culture which influenced their perception of freedom and government. This is relevant and shows up in things like the checks and balances (acknowledging man’s fallen nature), the idea of rights coming from God, and the importance of freedom of worship. More importantly one can see the implications when compared with other national socio-revolutions or outright revolutions around the same time period in which Christianity did not play apart: France, England and so forth. All over the world people were influenced by the Enlightenment (as was America) but the most successful experiments in self governance came from those countries which also were influenced by Christianity, and the most successful of these was America which was arguably influenced the most. So in the sense that many of our values, laws and principles which motivated and defined our independence, and founded our nation, could be argued to be derived from Christian principles, we could be called a Christian nation.
2) It is still true, by far, that the large majority of Americans self define as Christians. Does this mean they should exercise a tyranny? No, of course not; but it is a statement of fact which surely has some implications for our culture. In fact, I would argue that it is the presence of Christianity at our beginnings, and even today, which have made pluralism and religious freedom desirable and even possible in ways that other religious nations (such as islamic theocracies) or anti-religious societies (such as the Soviet Union or Red China of the 80’s) have not been able or willing to do. In other words it is because we are a Christian nation that Muslim’s, Jews, and atheist are all free to worship or not worship as they please, both publicly and privately. I’m sure this is an argument some of my friends on both sides of the aisle will despise, but I maintain that the Christian majority is a safeguard, not a threat to religious liberty. None the less, the only argument I’m actually making here is that you could call America a Christian Nation simply meaning that that defines the majority.
3) An implication of the above, which I believe must be allowed without fearing it threatens tyranny, is that the culture of America will necessarily have a tendency to reflect both the early and modern Christian culture which predominates. Christian churches are prevalent everywhere, Christian books, entertainment and so forth are an important niche. America benefits from the best aspects of Christian culture: orphanages, hospitals and many charities; the fact that we are among the most generous Countries; that fact that America was unique in it’s role in overturning slavery, combatting racism and avoiding caste systems of many kinds. This is not to say Christianity has alone been responsible for these good things, nor that Christianity has prevented any of these evils in the first place. The evil of slavery, and racism are real and horrendous dysfunctions in our development, but in these things America was not uniquely guilty, whereas the lengths to which America has gone to combat these things is, in many ways, unique. So, in the sense of our culture bearing unmistakable marks of Christianity, it is fair again to say America is a Christian nation.