People who contend that our country is a "Christian" nation are correct only in a limited sense. Many Americans are Christian, and many of those who built this country were Christian. But in a more basic sense, the American system is not Christian, and is, in fact, drastically opposed to biblical principles.
The primary purpose of the Constitution was to establish a form of government, and what it envisioned was something radically different from the ideal government envisioned in the Bible, where the ideal government (which the Christian faithful are hoping will one day come to be) is the "kingdom of God," headed by a king appointed by God himself or by a prophet of God. The people would have no voice in the selection of this "anointed one," or "Messiah."
In such a government, the laws would be handed down from God's king or God's prophets and imposed on the people, with no input from the people. That kingdom would ultimately govern the entire world: "Every knee shall bow."
In marked contrast, the U.S. Constitution established a government headed by leaders selected by the people themselves. The laws are to be made by representatives of the people by vote of the majority, and can be changed if the people vote to do so. The many laws in the Bible do not appear in the Constitution, and many would be in violation of it.
That is, the Bible envisions a theocracy, whereas the Constitution envisions a representative democratic republic. Those are incompatible ideas.
The radical Christian right, rather than praising the Constitution as a God-given system, should instead be condemning the Constitution and the government it set up as being against all biblical principles. To do otherwise shows complete ignorance of either the Bible or the Constitution.