As Dr. Joseph Waligore has pointed out, there were three notable figures from England who called themselves "Christian Deists": 1. Thomas Morgan; 2. Thomas Amory; and 3. Matthew Tindal.
They disregarded orthodox doctrines like the Trinity and the Atonement but still saw a special place for Jesus as Messiah.
We argue over which terms are proper. Sometimes it makes sense to attach a term to a movement that the thinkers did not use. For instance, the early "Thomists" or "Calvinistis" probably didn't use those terms to describe themselves (though such terms are entirely apt). However, the above three thinkers did accepted the label of "Christian-Deist."
Others, however with parallel views might not have self consciously understood themselves as "Christian-Deists"; but it still might make sense to attach such label to them. Thomas Jefferson, for instance, considered himself a "Christian" and a "Unitarian." He, like Franklin, tended to qualify his preferred version of "Christianity" with the adjective "rational" ("rational Christianity").
Jefferson did not, I don't think, consider himself a "Deist" and the only time of which I am aware he used that term, what he meant by it was the belief in one God. Hence Jefferson called the Old Testament Jews "Deists" because they believed in one God.
But in terms of openness to the supernatural doctrines of traditional Christianity (i.e., miracles) Jefferson was arguably less of a "Christian" than Morgan, Amory or Tindal were. Still, the label "Christian-Deist" may "fit" with Jefferson. (Or maybe Jefferson wasn't "Christian" enough, even though he understood himself to be one.)
The question then for whether it's appropriate to label the "key Founders" to be "Christian-Deists" is whether their beliefs mesh with the "Christian-Deism" as articulated by the above three: Morgan, Amory and Tindal.
With Ben Franklin, if we take what he detailed in the Samuel Hemphill affair as reflecting his personal creed, I think the answer is yes.
How this relates to Jesus. The "Christian-Deists" saw Jesus as Messiah, but in an unorthodox way. They were probably influenced by John Locke in this regard.
As I understand it they didn't worry about the Trinity or other orthodox doctrines. Rather, they understood there is a natural law determinable by reason. And some brilliant philosophers (Aristotle?) can get the results without Jesus, but with much intricate intellectual work.
In fact Franklin explicitly notes in
A Defense of Mr. Hemphill's Observations that before the coming of Jesus, "many would be able to save themselves by a good Use of
their Reason and the Light of Nature."
I guess this depends on
what it means by "many." That is, because man's reason is flawed
such that your average Joe Sixpack can't properly understand Aristotle and hence, many also
won't be able to save themselves by trying to live according to such principles.
Jesus
perfectly lived out and captured these principles in such a way that
ordinary people could understand and follow. This is what the
Christian-Deist concept of
Christianity republishing the law of nature
refers to. In fact, John Locke has a line about Jesus' teachings being
so clear that "ignorant fisherman" could follow them. So Jesus saves by
perfecting and modeling virtue and teaching it in such a way that everyone could follow and hence yields a net increase in moral practice.