In response, I would argue drawing a distinction between the "Deist" God and the "Judeo-Christian" God may be a false dichotomy. I raised a similar point in a brief dialogue with Kevin Schmiesing of the Acton Institute. The bottom line is Jefferson's God perfectly suits the role of the God that guarantees natural rights. Indeed, this makes sense given Jefferson authored the Declaration of Independence. And make no mistake, Jefferson's God was an active, intervening rights granting Providence. As Jefferson wrote in Notes on the State of Virginia :
And can the liberties of a nation be thought secure when we have removed their only firm basis, a conviction in the minds of the people that these liberties are of the gift of God? That they are not to be violated but with his wrath? Indeed I tremble for my country when reflect that God is just: that his justice cannot sleep for ever: that considering numbers, nature and natural means only, a revolution of the wheel of fortune, an exchange of situation, is among possible events: that it may become probable by supernatural interference!
Yet, Jefferson also rejected:
The immaculate conception of Jesus, his deification, the creation of the world by him, his miraculous powers, his resurrection and visible ascension, his corporeal presence in the Eucharist, the Trinity; original sin, atonement, regeneration, election, orders of Hierarchy, &c.
And I would argue the God of Jefferson was the God of J. Adams, Franklin, Madison, Wilson, G. Morris, Washington and Hamilton. There's room for some honest debate here. Those founders may not have rejected every single one of the above mentioned tenets Jefferson rejected (Adams for instance accepted the resurrection of Jesus of Nazareth, whom he believed a man, not an Incarnate God on the grounds that this was God doing for the most moral man what He one day will do for all good men, perhaps all men). I would argue even if there are no "smoking guns" proving beyond a reasonable doubt that for instance Washington, Wilson or Hamilton (until the very end of his life) believed in the tenets of American Founding political theology that I describe below, everything they said is compatible with it.
Here is how I summarized the God of the American Founding -- that common ground in which the above mentioned "key Founders" probably believed -- in a post that the Cato Institute reproduced:
Nature’s God was theologically unitarian, universalist (did not eternally damn anyone) syncretist (most or all world religions worshipped Him), partially inspired the Christian Scriptures, and man’s reason was ultimate device for understanding Him. He was not quite the strict Deist God that some secular scholars have made Him out to be. But neither was He the Biblical God. Rather, somewhere in between.
I would further argue that this God serves as a more authentic guarantor of natural rights than the orthodox biblical God. For one, the orthodox biblical God does not, by doctrine, guarantee natural rights as they are foreign to the Bible's text. As Robert Kraynak summed up America's Founding liberal democratic (or "republican" if you will) order & God:
Thus, we must face the disturbing dilemma that modern liberal democracy needs God, but God is not as liberal or as democratic as we would like Him to be.
[And for any potentially ignorant readers who erroneously think the concepts of "democracy" and "republicanism" are mutually exclusive, small l liberal, small d democracy refers to the Lockean principles articulated in the Declaration of Independence.]