Having defined a nation, according to Scripture, I will address the question as to whether or not the United States is a Christian Nation. Gary North recognizes the flaws in some approaches to this question:
There have been many detailed intellectual defenses of the United States as a Christian nation. These studies invariably rest on a conceptual error: equating state (civil government) with nation (society). That the United States has been a Christian society during its post-1788 period is obvious. This is not the same thing as the United States civil order when considered in terms of its defining judicial document, on which the United States rests its civil covenant.
In contrast, humanistic historians turn to the U.S. Constitution and point out that it is a secular document, and uniquely secular for the eighteenth century. They, too, confuse state with nation. They conclude that the United States is a non-Christian nation
To put it more succinctly, the question can only be answered effectively if you make a distinction between the official/legal status of Christianity and the informal impact of Christianity on the society as a whole. The latter is sometimes called the civil or civic religion, and carries no binding authority in the courtroom or chambers of legislatures, though it may include “official” recognition of God in the civil realm, such as in the phrase “In God We Trust” on our money or the mention of God in our pledge of allegiance.
Just because we were greatly influenced by Christianity in many ways does not mean we are now a Christian nation in any legal sense. Certainly the Mayflower Compact’s statement that the Pilgrim’s efforts were “for the Glory of God and the advancement of the Christian gospel” could be used to demonstrate the reasons the Pilgrims came to the USA, for example. In addition, all but one of the thirteen states had established churches or oaths of office requiring a witness to Christianity, prior to the ratification of the United States Constitution. Here are just a couple of examples:
I _______do declare, that I believe the Christian religion, and have a firm persuasion of its truth” 
Massachusetts Oath of Office
I _______, do profess faith in God the Father, and in Jesus Christ His only Son, and in the Holy Ghost, One God, blessed for evermore; and I do acknowledge the holy scriptures of the Old Testament and New Testament to be given by Divine Inspiration.
Delaware Oath of Office
Something, however, changed from the time the Declaration of Independence (1776) was penned and the Constitution (1788) was created, in that the latter refused to make official recognition of our prior Christian heritage. This is why the latter document makes no mention of God, according to North:
This new covenant meant a new god. The ratification of the United States Constitution in 1787-88 was not an act of covenant renewal. It was an act of covenant-breaking: the substitution of a new covenant in the name of a new god…. a “grand experiment” in which the God of the Bible was first formally and publicly abandoned by any Western nation.
John Lofton seems to agree:
Patrick Henry was one of the key anti-federalists and they were the ones who were, relatively speaking, really the Christian faction, and they opposed the Constitution in part because it gave short shrift to the Christian religion.
North argues that the Constitution was thrust upon the thirteen states illegally, as it was ratified in a manner contrary to the Articles of Confederation. Here was Article 13:
The Articles of this confederation shall be inviolably observed by every State, and the union shall be perpetual; nor shall any alteration at any time hereafter be made in any of them; unless such alteration be agreed to in a congress of the united States, and be afterwards confirmed by the legislatures of every State.
Instead of being ratified by the Articles Congress and state legislatures, the document was given to state constitutional conventions to ratify. Because the states had differing state churches, it is understandable that the framers could not set up a single established church for the whole country. This conundrum alone, however, does not explain the decision to deliberately omit recognition of our Trinitarian God in the document, nor does it explain Article Six, making the oath of office secular. The Articles of Confederation had made mention of “The Great Governor of the World”, so it was not unprecedented to have legal documents carry the recognition of our sovereign God.
Three Possible Marks of a Christian Nation
Before we settle on whether or not we are a Christian Nation, I must define Theonomy, the Establishment Principle, and the Judeo-Christian Ethic.
Theonomy is a system of thought that all nations are required by God to institute the Old Testament civil laws lest they be punished for breaking covenant with Him. Proponents have included R. J. Rushdoony, Gary North, Greg Bahnsen, George Grant and David Chilton. There have been varied approaches among theonomists as to how Old Testament civil laws might be instituted in a democratic republic, none of them undemocratic, as far as I can tell, though some on the left believe that having a religious basis for any law is verboten.
The Establishment Principle was debated among the founders of our country and was rejected in the 1st Amendment with the “Establishment Clause.” A range of views exist of this concept, including some who hold that the nation should be considered officially a Christian nation with a particular denomination being the representative of that Christianity. Others see establishment as simply the requirement that Christian magistrates carry their Christianity into the workplace with them.
By either of these two definitions, we are not officially “Christian.” Jesus has not been declared Lord, as has been the case in the United Kingdom, for example. Nor can it be argued that we have submitted ourselves to the Old Testament civil laws. So, using the standards of theonomy or the establishment principle we cannot conclude that the United States is a Christian nation.
One other concept, the Judeo-Christian Ethic, is sometimes used to make the argument that we are a Christian nation, but use of the prefix “Judeo” is problematic on several counts. First, it seems self-refuting. If the idea is that there exists some blending of two religions (Judaism and Christianity) then, of course, we are not a Christian Nation, but a Jewish-Christian Nation. But Judaism and Christianity are religions in conflict, because the one accepts Jesus, the Savior of the world, and the other explicitly rejects him.
Finally, a case can be made that the Christian consensus has largely disappeared, and pluralism has gained the upper hand, leaving just remnants of a Christian heritage found on early documents and courthouse walls. The widespread acceptance of psychological viewpoints about human behavior, the emphasis on material wealth over spiritual health, the focus on self in worship, the abandonment of a Biblical sabbath view, the rejection of children as a gift of God and the ascendancy of cultic or heretical views about Christ, the Bible, God’s Foreknowledge and the existence of hell have all contributed to the decline of any Christian worldview we once may have had.
Surprisingly, in some ways, the answer to the question of whether or not America is a Christian nation is irrelevant. As I will demonstrate in the next chapter, the focus in Scripture is godly governors and godly subjects, not establishing a Christian government. The only truly Christian nation is the Church. Just as France is made up of Frenchmen, a Christian nation is made up of only Christians, a nation without borders, and with Christ as her head.
Notwithstanding all that is said above, I am in essential agreement with the idea that an indelible mark has been clearly made by the Bible and Christianity on the American society and its legal system. There is no need to review that history here. We can be thankful for the freedom to worship and evangelize as Christians in this country. These facts cannot be denied by the atheist unevangelist. Turning on more lights won’t help the blind to see.
To sum up: we are a Christian nation only in an informal sense and that only in so far as we retain the consensus of Biblical values. That consensus is quickly disappearing among people.
This article is drawn from the book, With Christ in the Voting Booth.
 Gary North, Conspiracy in Philadelphia: Origins of the United States Constitution (2004) Online Version, p. XVI
 http://undergod.procon.org op. cit
 North, op. cit.
 John Lofton, quoted in Gregg Jackson and Steve Deace (2011) We Won’t Get Fooled Again, JAJ Publishing
 I would argue that much of the American political/legal system has its roots in these laws, such as the right to subpoena, the distinction between murder and manslaughter, the importance of making restitution, and a host of other comparable laws, too numerous to mention here.