They wouldn't have thought that moral law needed any input from the masses, since it came from God.
No doubt, there were some Christians amongst the deliberators, but it can easily be seen that the majority of them were well informed about the horrible religious controversies that had plagued the colonies for almost 200 years, and they were looking for a compromise.
But compromise is not possible among revealed moralities, and it must have become obvious that the only way out of the thicket of competing beliefs would be to move the discussion to neutral ground with laws made by democratic means.
This, to me, after a lot of thinking, talking, and debating, seems the most likely explanation for the removal of all references to God in the Constitution, the denial of any religious test for office, and the refusal to allow any state establishment of religion.
Many of the founders called themselves Deists, but this was a protective label, in these years so soon after the witch trials, and was cover for those who had worked out the need to establish a new way to govern through continuous revision of government: they called it democracy.
It's stood us in good stead, and now with the advancement of neuroscience, and a better and better understanding of both the need and genesis of religious belief, but concurrent with the obvious need for a common ground of morality based on that neuroscience and evolutionary psychology, we may be approaching a final resolution of the church/state controversy, in favor of the Founders' original intents, arrived at long ago, from careful reviews of the history of governance.