In probably the most well-written exposition I've seen, no, the US was not established as a Judeo-Christian nation.
In fact, in a treaty signed by 23 senators and President John Adams, you'll find these words:
As the government of the United States of America is not, in any sense, founded on the Christian Religion...Does it get any clearer than that? And what was the public reaction to these very clear words?
I found the treaty and Adams' statement reprinted in full in three newspapers, two in Philadelphia and one in New York City and, in one case, held the actual newspaper (the Philadelphia Gazette and Universal Daily Advertiser for Saturday, 17 June 1797) in my hands. There is no record of any public outcry or complaint in subsequent editions of the papers.So let's hear it for freedom of religion in this country!
If God himself didn't see fit to coerce anyone into a religion, then it's certainly antithetical to what God himself practices that some people would try to force others into their beliefs. Freedom of will - an oversight by God, or a wise practice?
The nation was founded on individual liberty. Liberty in speech, religion, assembly, property, etc. Therein lies the basis for this nation's morality. Live free, and respect the right of others to live free as well.
If our nation's laws were based on biblical law, well, we're missing quite a few. Where's that "Honor your parents" law? Where's that "Keep the sabbath holy" law? The pentateuch is hardly represented in American law - at any point in history.
Yes, murder is against the law here in the US, and murder is against the commandment of a biblical God. But it's US law not because God said so, but because it robs a man of his liberty. As does stealing. And while a few laws might appear to be based on Judeo-Christian laws, was it because God said so, or was it because that simply looked like best practice and common sense, based upon our nation's foundation of protecting individual liberty?
The words in that treaty were "quite well accepted, only a few years after first the Constitution and then the First Amendment were ratified, that 'the Government of the United States of America was not, in any sense, founded on the Christian religion.' After a bloody and costly civil war and the passage of the Fourteenth Amendment determined that citizens of the United States cannot have their rights abridged by state or local governments either, religious liberty for all was established. Governmental neutrality in matters of religion remains the enduring basis for that liberty."
A government neutral in matters of religion is the most sound basis for protecting religious freedom. If you choose to believe that government should be used to coerce Christianity into law, then you're no different than the socialist who wants to use government to limit a person's income. You're both statists, and neither of you believe in liberty.
(And for those who trot out the canard about "license," I challenge you to show me where license is discussed in the Constitution or the Bill of Rights. The country's founding documents are not living documents for you to alter as you wish. They weren't concerned about license, and from a civic perspective, you shouldn't be either. The founding fathers considered liberty to be sacred, and so should you, even if it means that people might choose behaviors that you don't approve. I'll refer back to God's everlasting best practice of giving us freedom of will...)