As much as I like Jefferson politically, I think Jefferson is a good example of what was wrong with Enlightenment thinking about religion. What Jefferson fails to understand is that just presenting a morality isn't enough, it is also essentially to present a reason to follow that morality. In the case of the New Testament, the basic reason is: Jesus and God can do miracles, therefore they are the alpha-male leaders, therefore they should be obeyed. This reasoning is sound, given the human primate instinct to obey alpha-males. Remove the miracles and the whole thing falls apart since there is no reason to follow the morality.
The Old Testament takes a somewhat different approach. The Old Testament says that the forces of history eventually punish immoral cultures, and the forces of history can be personified as God who then resembles a slow-acting alpha-male. So here the same alpha-male concept is used but without reliance on miracles. Unfortunately the Old Testament approach turns out to be too abstract for most people, so the New Testament approach is more effective.