Check out a comment that Dr. David Mazel left comparing the wording of the Mayflower Compact and the US Constitution; the difference is like night and day. If our Founders intended the US to be a "Christian Nation" in a public or civil sense, the wording of the Constitution would have looked a lot more like that of the Mayflower Compact.
I always address the "Is America a Christian nation?" question early in my American literature classes. Instead of asking them simply to answer the question, I ask my students what "Christian nation" might mean, and which of the meanings might make sense when applied to the United States.
Does it mean "Most Americans are Christians?" Then perhaps America is a Christian nation. But then, what does it mean to be "Christian"? Do most Americans (or the nation as a whole in, say, its foreign policy) exemplify the pacifism and anti-materialism of the Sermon on the Mount? Of course not.
Or does "Christian nation" mean a nation founded upon Christian principles and toward Christian ends? This is the point at which I have the students read and compare the wording of two charters, the Mayflower Compact and the U.S. Constitution:
The Mayflower Compact (1620)--"In the name of God, amen. We, whose names are underwritten . . . having undertaken for the glory of God, and advancement of the Christian faith, and the honor of our king and country, a voyage to plant the first colony in the northern Parts of Virginia; do by these presents, solemnly and mutually, in the presence of God and one another, covenant and combine ourselves together into a civil body politick, for our better ordering and preservation, and furtherance of the Ends aforesaid."
The Preamble to the United States Constitution (1787)--"We the people of the United States, in order to form a more perfect union, establish justice, insure domestic tranquility, provide for the common defense, promote the general welfare, and secure the blessings of liberty to ourselves and our posterity, do ordain and establish this Constitution for the United States of America." (I also throw in Article VI, Clause 3: “no religious test shall ever be required as a qualification to any office or public trust under the United States.”)
The first gives us a crystal-clear example of how a charter is worded by people deliberately founding a Christian polity. We are told directly that the colony is being "undertaken for the glory of God, and advancement of the Christian faith." The Founding Fathers could have used similar wording, but didn't. The rationales for creating the Union is purely secular: insuring tranquility, providing for defense, promoting the general welfare, and securing the blessings of liberty.
Certainly the United States is not a Christian nation in the sense in whic Plymouth was a Christian colony. Still, some students typically insist that it is a Christian nation in some other sense, in a way that falls short of the Plymouth standard yet means more than the mere demographic fact that most Americans identify themselves as Christians. Funny thing--they can never seem to figure out what sense that is, though.