Ed Brayton's got the goods. Just put up next to the Ten Commandment's display words taken from a Founding Era Treaty -- 1796 Treaty with Tripoli: "The government of the United States of America is not in any sense founded on the Christian religion."
Speaking of Founding Era treaties, that statement is actually in the body of the Treaty -- Article 11. Contrast that with the 1783 peace treaty between US and Great Britain which preamble begins, "In the name of the Most Holy and Undivided Trinity. It having pleased the Divine Providence to dispose the hearts...." That language is not in the body of the treaty, but in the preamble. As Chris Rodda put it:
This reference to the trinity was not an acknowledgement by the government of the United States that America was a Christian nation. It was an acknowledgement by the government of Great Britain that England was a Christian nation. "In the name of the Most Holy and Undivided Trinity" was the customary way that England, like most of the Christian nations of Europe, began their treaties and other documents. The agents of the United States had no control over this wording.
Further, consider that the three diplomats who signed this treaty for the US were John Adams, John Jay, and Benjamin Franklin. Adams and Franklin were fervent theological unitarians, and Jay, at least in one letter, doubted the Trinity's "orthodoxy."
Those three, as a group, were the furthest thing from "orthodox Trinitarian Christians."