I think there are three issues that must be dealt with here.
First there is the theological/Biblical question. Does the Bible actually teach that there is such thing as a Christian "nation"?
Second there is the historical question. Was this nation founded as a Christian nation? Or was it founded as a secular nation? Or was it founded by professing Christians who believed in a seperation of church and state?
Third there is the current question. Does America today behave as a Christian nation?
In my opinion how a person answers question one will determine how they answer questions two and three. I said this was a trick question, and it is. Why? Because the answer to question one "Does the Bible teach that there can be a Christian nation" is no. The only Christian nation that will ever exist will be the New Jerusalem in which the Messiah Himself will actually rule. Those who claim that America, or any other nation, is/was a Christian nation must confront the first question more carefully. After all America is not the first, or only, nation in the history of the world to have some claim it is a Christian nation. However the Bible never speaks of a Christian nation nor does it teach that there can be a Christian nation. There can be no doubt that many of the American founders were professing Christians* and there can be no doubt that they wanted a country that was friendly towards Christian teachings (while maintaining a level of seperation of church/state). However that does not mean that America was, or is, a Christian nation. Why not? Because such a thing does not exist Biblically.
Even if the Bible did teach the concept of a Christian nation it is unlikely that America would fit the bill. From the African slave trade in early America, which John Wesley called the worst kind, to the continued religious/political/economic justifications of slavery until after the Civil War, to the practice of abortion on demand (a practice protected by the government), the legal status of pornography, adultery, fornication, homosexuality, unjust government officals, etc, etc. America is not a Christian nation. America is certainly, in my opinion, the best country on the face of the earth. I would not live anywhere else even given the chance to live some other place for free. However that does not mean America is a Christ-like, or Christian, nation. This is simply because (a) the Bible does not teach such a concept and (b) America simply does not behave like a Christian nation.
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*I use the phrase "professing Christian" realizing that many of the founders were not orthodox Christians.