"T. David Gordon is a minister in the Presbyterian Church in America and associate professor of religion at Grove City College (Grove City, Pennsylvania)." He writes a good article that explores issue of orthodoxy and Christian America. On "Christian America" he writes:
Especially surprising, in this regard, is the amount of effort expended at attempting to prove that our early Republic was intentionally "a Christian nation" or that the individual Founders were Christian believers. (3) This surprises me not only because the existent documents appear to be at best inconclusive, but also because it would mean nothing anyway. The accidents of history can never oblige us; and even if the Founders had intended to establish a Christian nation (whatever that might mean), we would be under no obligation whatsoever to continue the experiment in our generation, unless we (the populace as a whole) believed there was value to it. To illustrate: The Founders also plainly intended to permit the African slave trade to continue for the foreseeable future without federal interference. Does this mean we should resurrect the practice today? Of course not; it was a horrible idea then, and would remain a horrible idea today.
And on George Washington's creed in particular he writes:
There are many sources for this. In popular media, one naturally thinks of the late D. James Kennedy at Coral Ridge; and at a more academic level, the 1,200-page treatise by Dr. Peter Lillback of Westminster Seminary, George Washington's Sacred Fire. My own opinion is much more of that associated with Michael Novak (Washington's God), Paul F. Boller, Jr. (George Washington and Religion), or my colleague Gary Scott Smith (Faith and the Presidency: From George Washington to George W. Bush), each of which describes Washington as neither a conventional orthodox Christian nor a conventional Deist, but some kind of a hybrid between them who believed in a Supreme Being who acts in history (unlike a strict Deist), who almost never mentioned Christ, and certainly never mentioned any redemption achieved by him (unlike a genuinely orthodox Christian). I am content to think of him, as Dr. Smith does, as a "theistic rationalist."
One pleasant thing I've discovered covering the "Christian America" controversy is that that thesis doesn't speak well to many notable evangelical scholars.