Apparently, about a month into the difficult deliberations, Ben Franklin proposed that the Convention (which to that point hadn't offered a public prayer of any kind) do a little praying. The rest of the Founding Fathers weren't interested. The motion apparently didn't even get a vote. Apparently, when the chips were down--when this country was being founded--public prayer was deemed "unnecessary."
No (public) prayers to any God during the Constitutional Convention
"Franklin's motion for prayers in the Constitutional Convention has been used as the basis for another clerical falsehood that has been presented to the eyes or ears of nearly every man, woman and child in the United States. We are told that, the Convention for a month opened its sessions without prayer, that at the end of this time nothing had been accomplished, it was in a state of confusion, and on the point of adjourning, when Franklin came forward, proposed that the sessions be opened with prayer, which was adopted, after which the work of the Convention was speedily and successfully performed. This is adduced as a striking proof of the efficacy of prayer. The fact is, there was not a prayer offered in the Convention from the time it convened until it closed. So nearly unanimous were the members in their opposition to Franklin's proposition that not even a vote was taken on it. Franklin himself, referring to it, says: "The Convention, except three or four persons, thought prayers unnecessary."