I note that along the spectrum of plausible meanings of the phrase The United States was founded on Christian principles, the only ones likely to be adequately rebutted by scouring the Constitution for references to God are pretty narrowly clustered at one end.
Explicitly, yes. Implicitly, no. After all, if this nation was "based on Christian principles" one would expect reference to those principles in some form or another. There is none. In particular, one sees no reference to Jesus or God. For example, the one place it would surely exist in the explicit statement of the oath of the President. It does NOT end in "so help me God." Thus I argue that the document, taken as a whole, screams out secularism.
By the way, you have posted some excellent posts here. I have found myself checking my own preconceived notions along the way. Thanks a lot.