Here is a taste from Dr. Fea's personal blog:
... And yes, one can be a theist and reject all the tenets of Christianity. One could certainly believe in a God who intervenes and providentially orchestrates the world without believing that that God revealed himself in the form of a human who died for the sins of the world. What I am basically doing (and I am giving a bit of my book away here) is trying to argue that the founders were neither deists or Christians, but something in-between. Some scholars have suggested that they were "theistic rationalists." I think this is a fair term (although I am not sure I use it in the book).
The larger truth that I've been pressing for years: We've got two boxes "Christian" and "Deist" each of which can have narrow or broad meanings. The narrow meaning of "Christian" is someone who believes in the Trinity and cognate orthodox doctrines, that the biblical canon is inerrant or infallible, etc. The narrow meaning of "Deist" is someone who believes in a non-intervening clockmaker God who does not reveal anything to man in any Holy Book. What a wide gulf between those two concepts! It shouldn't surprise that many Founders wouldn't fit into either box, but be somewhere in between.
The game that scholars or advocates can play is define one box strictly and one box broadly in order to capture a particular founder for a preferred outcome. Strictly speaking the first four Presidents and Ben Franklin were neither Christians nor Deists (with some admitted uncertainty regarding Washington and Madison). Broadly speaking they were both Christians AND Deists.