First, one must define what they mean by a "Christian" nation?
If you mean a nation that was deeply and profoundly shaped by Christian beliefs and values, and a nation in which the church had a major role in the shaping our forms of culture and government, then the answer is a qualified yes. America is a Christian nation only in this very limited sense.
The majority of early Americans were sympathetic with most Christians ideals. But, and this is rarely noted the overwhelming majority of Americans (1790) did not go to church at all, some estimating the percentage to be as high as 90% before the First Great Awakening. The number today still exceeds 30%.
But this idea that America was Christian in some sense must be qualified precisely because Enlightenment Deism also had a major role in shaping America. Our founders clearly drew language and ideas from both sources, for which I personally thank God! If you know anything at all about the history of religion in Europe (with the bloody wars of religion), and in early America (with its intolerance of non-Christians and Christians who were not mainstream, like Quakers and the Baptists), you know that this mixture was one that gave us a very different land over time. Here church and state were separate for a good reason. Faith could flourish here, and it has more than in any modern nation. But I argue this is precisely because the state has not had a role in advancing the faith, any faith. This must remain so even with non-Christians growing in number in the present age.
Second, in what sense could any nation be considered a "Christian" nation?
A nation could not be Christian in terms of being the church because a nation is not synonymous with the church, never ever. This is a mistake made in the aftermath of the (Holy) Roman Empire, at least in linking the Vatican with the state in direct ways, a mistake which should not be made again. Rome recognizes this reality now but many fundamentalists still do not see or understand why.
A nation could not be Christian in the sense that Christians should govern it to the exclusion of others or it would violate the very principles of the kingdom of Jesus in this present age. We are not called upon to build a theocracy, or a nation-state that is under the sovereignty of King Jesus, constitutionally.
If you think my last sentence is silly you do not know the history of ideas in America. There were Christians in our founding era who wanted to insert the name of Christ into our founding documents. This failed and I am grateful it did. All one really needs to do is look at Puritan New England (Massachusetts will do as a model) to see how much this idea failed in real practice. I once asked a leading theonomist where we should go to discover the "closest" historical example we have to what he hoped to see come about in the future and he answered "Puritan New England." I rest my case. Massachusetts was a Puritan commonwealth and this idea failed miserably. I would not have wanted to live in Massachusetts prior to the 1820s. Give me Rhode Island, Pennsylvania or Virginia as an alternative, at least for political reasons.
Third, why should we desire a Christian nation given the history of how Christians have used power and influence in so many ways that have fallen short of the will of Christ? There are two cities, as St. Augustine noted centuries ago, and the two cities should never be linked in a direct way.
Should Christians influence culture? Absolutely. Should they run for office? Yes, for sure. Should they seek to make the public square a place where religion is treated fairly? Yes, without doubt. But the idea that we were ever a "Christian nation," or ever should be one, needs to be assigned to the dust bin of historical ideas tried and found wanting.
So long as non-Christians hear this kind of talk from far-right Christians they have every reason to resist what they see as a potential encroachment upon their political, religious and social rights. Liberty is a grand experiment. We have enjoyed it for 220 years constitutionally. We have a great system of government, as one of the founders noted, if we can keep it. It will take Christians and non-Christians to preserve it. Right now some Christians (a minority I am quite sure) seem intent on preserving it by destroying it so that they can remake it in their own way. Preserving our system of laws and government will involve the continued freedom the church needs to make disciples and publicly enjoy the freedom of religion. It is right that we argue for this freedom, even to the Supreme Court. It can be lost and vigilance is necessary. But this is not what many on the far right argue for if their blogs, Web sites and magazines are read carefully.