No the U.S. is not specifically a Christian nation. There are synagogues that were established here long before many Christian denominations.
Before the Constitution there was the Declaration of Independence where the writer did not refer to God as Jesus but did acknowledge a belief in a Supreme Being. Throughout the document a reference to God is made four some say five times. I'll start off with two that are connected, "
Laws of Nature and of Nature’s God". Who is responsible for “the laws of nature” but God......certainly not man nor nature itself? From the “laws of nature” sprang an awareness of natural law sometimes called common sense which we seem to be in real short supply these days. It was understood by early philosophers to be a source of higher law that never changes. Nature's law is best explained by Cicero, a Roman politician, as early as the 1st Century B. C. and whose philosophy influenced the Founders. Of course what Cicero wrote predated the existence of Christianity when he stated “Nor may any other law override it, (Nature's Law) nor may it be repealed as a whole or in part… Nor is it one thing at Rome and another at Athens, one thing today and another tomorrow, but one eternal and unalterable law, that binds all nations forever.” Of “Nature’s God,” the second reference to deity is, of course, more explicit and needs no explanation.
The third reference to God in the Declaration of Independence is the word
“Creator” found in the second paragraph. “We hold these truths to be self-evident, that all men are created equal, that they are endowed by their Creator with certain unalienable Rights, that among these are Life, Liberty and the pursuit of Happiness.” This boldly identified our base for at least three unalienable rights as God, and the Founders identified this truth as self-evident. Any person endowed with common sense or reason (as Cicero explained in the laws of nature) should come to this conclusion without difficulty.
The fourth and fifth references to God are found in the last paragraph. “We, therefore, the Representatives of the United States of America, in General Congress, Assembled, appealing to the
Supreme Judge of the world for the rectitude of our intentions, do, in the Name, and by Authority of the good People of these Colonies, solemnly publish and declare, That these united Colonies are, and of Right ought to be Free and Independent States, that they are Absolved from all Allegiance to the British Crown…”
The fifth and last reference to God asks for God's divine protection in our course of action. “And for the support of this Declaration, with a firm reliance on the protection of
Divine Providence, we mutually pledge to each other our Lives, our Fortunes, and our sacred Honor.”
There was no dissent noted with respect to these references to God in this document by any of the participants then, nor should there be now.
The Founders understood in order to have a self governing system it requires people to be of good moral character. Something quite lacking in today's society which requires more laws to be implemented and with each new law freedom is lost.