Well said WordSwordsman.
Et al, I didn't know we were talking about whether the U.S. was a Christian state theocracy, for example, like Spain. In Spain (at least up to 1979 when I was last there), if born there you were to be raised Catholic per joint State/Church control. I know this because I almost got married to a Spanish national then, and would have had to sign a legal document saying I would raise my children in the Catholic Church. That was enforced by the government of Spain. Legal marriage and divorce was only decided by that joint authority also. Of course not all people followed the Catholic Church of Spain in their lives, but legally, they were still under its power and influence there. The United States was never meant to be like that, and that's not all what it means to be "a Christian nation" anyway.
When the majority of the people join together and agree to be ruled by Christian principles from The Bible, especially Christian principles from Christ as a moral device in interpreting and administering the law, then that most definitely is evidence of a Christian nation. I don't expect later generations after the '60's are much aware of America's early history of using Christian principles as that method of measure, so the condition of the U.S. today can hardly be compared to that early history, especially the times of the American colonists.
Researching the 'Blue laws' is a good way to discover just how many states in the U.S. enforced Sabbath day laws, which is one such evidence of the people in individual U.S. states deciding what laws they will live under. There's still dry counties in my state where alchohol cannot be bought or served on Sundays. That comes from Christian Sabbath interpretation influence upon local law. There used to be a lot more counties in my state that observed those blue laws on Sunday, not that many decades ago.
Now a good question would be, just how could the states and local governments enforce those Blue laws back then and not have the Federal government step in to say they can't? Because like WordSwordsman said, the 1st Ammendment of the U.S. Constitution protects the people's religous freedoms. It's groups like the ACLU, etc., that have been busy abusing the Federal system to stomp upon states rights to try and prevent Christians from exercising their Constitutional right to freedom of religion and religious speech (i.e., Judge Roy Moore's stance in Alabama for having a Ten Commandments monument on public soil). Per the U.S. Constitution, there's something like 17 specific powers the Federal government has authority in over the states, but all other powers are reserved to the states themselves and to the people. Many today have forgotten that separation of powers.
In the early American colonies, the centers of learning, universities, were run by the Churches. This is why many of the oldest U.S. universities are still connected with the Churches. And quite a few them have very liberal programs now, some even outright teaching socialism and non-Christian principles, just for education's sake. That's a litmus check on how far away from Christ many in our nation have fallen today. So just because it's difficult today to see the U.S. as a Christian nation, or because socialists/atheists or groups like the ACLU deny it ever was, they have yet to destroy all the evidence that the U.S. was once a Christian nation being governed upon Christian principles. And who today is going to take the time to go back in history of the U.S. to find that out? It's much easier to just agree with the media and history revisionists.