Jefferson on Deism, His Definition May Surprise You:

Everyone who has read my work knows that I've long pondered the Founders & Deism issue. My research has led to some surprises. One issue I'm still grappling with is whether it is proper to categorize someone as a "Deist" even if he believed in an interventionist God. In this day and age, we've come to associate Deism with the belief in a cold, distant, non-Intervening Providence. Yet, surprisingly, many of the men we associate with Deism, notably Jefferson and Franklin, spoke of a warm intervening Providence.

On one thread, I remember explaining to someone that many of the men who understood themselves to be Deists believed in an intervening God. For instance Ben Franklin, as far as I know, never referred to himself as anything other than a Deist in his adult life, also remarked

I have lived, Sir, a long time, and the longer I live, the more convincing I see of this truth: that God governs in the affairs of man. And if a sparrow cannot fall to the ground without His notice, is it probable that an empire can rise without his Aid?

But Franklin still understood himself to be a Deist (I think). One commenter on the thread where I noted this replied that since Deism by definition posits a non-Intervening God, Franklin et al., must have been confused as to what they really were.

But that's only if today's present dictionary definition of Deism matches how the "Deist" founders understood themselves. It could very well be that Deism became to mean utter rejection of all Revelation and belief in a strict non-interventionist God some time after the Founding, as a later progression in the Enlightenment.

But anyway, here is Thomas Jefferson's definition of Deism in an 1803 letter to Dr. Benjamin Rush:

II. JEWS. 1. Their system was Deism; that is, the belief of one only God. (my emphasis) But their ideas of him & of his attributes were degrading & injurious.

....

1. [Jesus] corrected the Deism of the Jews, confirming them in their belief of one only God, (my emphasis) and giving them juster notions of his attributes and government.

So according to Jefferson, Deism simply means belief in only one God, which indeed seems to be an early, commonly accepted definition of Deism. Similarly (small u) unitarianism simply means disbelief in the Trinity. The Capital U Unitarians were a sect of the Congregational Church (to which John Adams belonged).

And the terms "Deist" and "unitarian" seemed to be used interchangeably to describe those, like our key framers, who believed in one God but wanted to understand Him on rational grounds and hence broke with many of the traditional Christian orthodoxies. And these terms "Deist," and "unitarian" were not, according to founders like Jefferson and Adams, mutually exclusive with "Christian." Indeed according to such founders (following Joseph Priestly) Christianity had been corrupted through dogma, and that corruption was not only represented in clerical dogma but also in the Bible itself whose entire history was "defective and doubtful" in Jefferson's words and contained "errors and amendments" in Adams's (thus it was not inerrant).

These corruptions included doctrines like the Trinity, the Virgin Birth, predestination, eternal damnation, many of the miracles in the Bible which seemed to defy reason and science, and many others.

Christianity, free from such corruptions, would be in complete congruence with the Deistic and unitarian teachings to which our key founders adhered.

Russell Kirk's definition of Deism, in The Roots of the American Order, seems pretty on the mark, for the Founding, except for the passage which I've it italicized:

Deism was neither a Christian schism nor a systematic philosophy, but rather a way of looking at the human condition; the men called Deists differed among themselves on many points....Deism was an outgrowth of seventeenth- and eighteenth-century scientific speculation. The Deists professed belief in a single Supreme Being, but rejected a large part of Christian doctrine. Follow Nature, said the Deists (as the Stoics had said before them), not Revelation: all things must be tested by private rational judgment. The Deists relied especially upon mathematical approaches to reality, influenced in this by the thought of Sir Isaac Newton. For the Christian, the object of life was to know God and enjoy Him forever; for the Deist, the object of life was private happiness. For the Deists, the Supreme Being indeed was the creator of the universe, but He did not interfere with the functioning of His creation. [my emphasis] The Deists denied that Old and New Testaments were divinely inspired; they doubted the reality of miracles; they held that Jesus of Nazareth was not the Redeemer, but a grand moral teacher merely. Thoroughly rationalistic, the Deists discarded all elements of mystery in religion, trying to reduce Christian teaching to a few simple truths. They, and the Unitarians who arose about the same time, declared that man was good by nature, not corrupt; they hoped to liberate mankind from superstition and fear.

Save for the part on the Creator not interfering with the functioning of His creation, Kirk's definition is pretty close to the "Deism" of the Founding. It would be more accurate to say that Deists like Jefferson, Adams, and Franklin (and probably Madison and Washington) didn't believe in the Miracles and other behaviors attributed to God found in Revelation which contradicted the laws of Science and Reason. Therefore when God did intervene, He did so while acting consistent with the laws of Science. He did not for instance, walk on water, part the Red Sea, or turn Lot's wife into salt. This explains why the Deists, like Jefferson and Adams could shirk at some of the Miracles and Prophesies recorded in the Bible which seemed so far fetched, but still believe in a God who intervened in the affairs of men. Essentially they believed in a God who did play dice with the universe.

What I'm looking for is founding era writings which understands "Deism" as active belief in a non-interventionist God. Also, I know little of the thoughts of Thomas Paine and Ethan Allen, both of whom embraced the term "Deist." Did they argue for this?

Finally, see this excellent article by Gregg Frazer who argues for a new term to describe the beliefs of Jefferson, Adams, Franklin, Madison, Washington, and others: Theistic Rationalists.