Well, expect a lot of screaming that the Constitution is secular. And by formulation it is. Maybe part of the reason for that is a sense of shame at how it accommodated chattel slavery, and they did not want to put a lot of references to God cheek-by-jowl to that. Men knew this was an ungodly compromise in that sense, although embodying great ideas in other senses.
It was secular, but not really in the modern sense of the word. Back then, secular was often used to simply mean things that weren’t directly governed by some church or spiritual authority, not things that were wholly separated from religion or religious ideas.
The King of England, for example, would have been seen as a secular position, even though he also was the “Defender of the Faith”, was required to be a Christian, and had to fulfill certain religious duties. The fact that he wasn’t appointed by any religious authority, and his activities were independent of them and not directed by them was enough to differentiate that position as “secular”.