I believe the answer is No is three important ways.
1) Our Government, and its guiding documents, are intentionally secular. It is a principle of our country that there are no Governmental religious tests for citizenship or leadership. While it is important we do not try to eliminate faith or acts of faith from political leadership, it is equally important that we do maintain an appropriate separation of church power and political power. This is part of the checks and balances our country by and large does so well. Furthermore as a very serious Christian I believe that historically when the church has pursued governing power it has generally ended up losing it’s soul, so to speak. It is our Lord who encouraged us not to seek power, but to seek humility and service and meekness. So if Christian nation means Christian government, then no we are not a Christian nation.
2) There is no true tendency towards a theocracy, nor should there be. Questions for example of abortion or homsexual marriage, while influenced by personal convictions and faith on all sides, are not actually decided according to a Holy book. In truth Christianity is not a threat to pluralism, but is rather the protection of it. It is my perception that it is because of our Christian culture that America offers more true freedom of thought and religion than any country int he world. It would be extremely detrimental to both Christianity and America if America were to attempt to be a theocracy today. Neither Christianity (nor Judiasm for that matter) has never been properly about any kind fo forced conversion. Christianity is about lives changed from the inside, not controlled from the outside. One may gain a similar appearance of behavior in either case, but apart from appearance there is no similarity at all. Here again, we are not a Christian country.
3) The ideals of America, while influenced by Christian principles, and even compatible by and large with them, are not, in fact identical to Christian ideals. Being Christian, and being American are not synonomous. It is bad for the church when we equate good American principles like democracy or capitalism with scripture (which speaks directly of neither) or even more arguable principles like strict individualism (which scripture speaks of in the extreme as a negative); Nor is Christianity limited to or even dominated by American Christians. For us to believe that Christianity is an American religion (which is not the same question but related) is to perpetuate an unfortunate misconception many unbelievers share that Christianity is exclusive rather than openly inclusive of all who will come. Similarly America is not a Christian nation if by that we mean that non-Christians are less welcome or valuable; in any way second class citizens to Christians.
America is a grand country with noble ideals, many compatible with but not owned exclusively by Christianity and one of those ideals is a grand inclusiveness, a pluralism which truly blends not in a multicultural stir fry, but in a melting pot of cultures producing something new and special, something called being American.