A friend emailed arguing for a broader definition of "Deism." Indeed, scholars have used terms like "warm Deism," or "Providential Deism" to describe the religion of Washington, Franklin, etc.
Thomas Jefferson, from what little he wrote on Deism, seemed to endorse a very broad understanding of Deism, that is belief in one God. He wrote of the "Deism" of the Jews.
In an 1803 letter to Dr. Benjamin Rush, Jefferson wrote:
II. JEWS. 1. Their system was Deism; that is, the belief of one only God. 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, and giving them juster notions of his attributes and government.
According to Jefferson, Jews, Muslims, Unitarians, Christians are all "Deists," because they all worship one God. Well...maybe not Trinitarians because they worship three gods. :)
Jefferson's understanding of "Deism" is arguably too broad to be meaningful. And, also arguably, an understanding of "Christianity" that holds anyone who calls himself a Christian (even if an agnostic or an atheist) is too broad to be meaningful.
Scholars can also unfairly play the broad/narrow game to unfairly claim the religion of the American Founders for the side they desire.
As I wrote on Secular Right's website comment thread:
... One unfair thing scholars from both sides do is read one term broadly and the other narrowly to try and “capture” a Founder for each respective side.
The broad understanding of Deism includes belief in an active personal Providence. The broad definition of Christianity includes anyone who call himself a Christian or is formally/nominally associated with a Christian church.
The narrow definition of Deism means belief in a non-intervening God. The narrow definition of Christianity requires strict adherence to the orthodox Trinitarianism found in, for instance, the Nicene Creed.
Broadly understood, the “key FFs” (the first 4 Presidents, Ben Franklin and a few others) were both “Christians” and “Deists.” Hence David Holmes’ term “Christian-Deism” to describe their creed. Narrowly understood they were neither. Hence terms like “unitarianism” or “theistic rationalism” to describe this creed.