Michael and Jana Novak have responded to Joseph Ellis' thoughts on the Founders and Religion on the Encyclopedia Britannica Blog. (See my thoughts on Ellis' post.) In particular, they don't like Ellis' use of the phrase, "pantheistic sense of providential destiny," to describe Washington's God. They write:
Finally, it is really not possible to demonstrate from Washington's public decrees that the Providence to whom he asked his army and fellow citizens to pray was "pantheistic." On the contrary, his public prayers as commanding General and as President expected Providence to favor liberty and thus, though both prayed to the same Providence, the American cause over the British. He expected his God -- and the nation -- to "interpose" his divine action in the course of the war, and in the later course of American history.
And just as the American Founders held that the natural rights they declared belonged not solely to them but to all humankind, so the God to whom they prayed did not belong solely to them, but is the Almighty Lord of all, who sits in judgment over this nation and others. President Washington did not scruple, in his eloquent message to the Hebrew Congregation of Savannah, to identify the God "Jehovah" who led the Jewish people in Israel, with the Providence who led Americans through their founding period.
I think "pantheistic" aptly describes not just Washington's, but the other key Founders' God. Though It was, as the Novaks' note, a particular type of pantheistic Providence; theirs was an active personal God, indeed one who favored political liberty and frowned upon tyrannical leaders (not exactly attributes of the Biblical God, who doesn't seem concerned with political -- as opposed to spiritual -- liberty; and Paul admonishes Christians to follow civil magistrates, even secular, pagan, and arguably tyrannical ones like Nero, the leader to whom Paul told Christians to obey in Romans 13).
The Founders' God was, however, universalistic. Various peoples of various religious traditions, even those outside the "Judeo-Christian" one, worshipped the same God who goes by many different proper names. And it was customary for the Founders to use the proper name for God with which the addressees would feel most comfortable. The only time Washington ever, to my knowledge, named God "Jehovah" was in one address to the Hebrew Congregation of Savannah. Twice however, I have counted Washington used the proper name "the Great Spirit" -- here and here -- for God, but only when addressing American Indians.
In sum, if "pantheistic" can mean an active, personal, universalistic God, then such a term accurately describes the God the key Founders like Washington worshipped.