Nope. The abundant witness of the Founders was that a bible philosophy, which robustly stands for what I just outlined, is the only valid moral foundation for this constitution. Never ever confuse means with ends. It is literally glory of God or bust.
The founders of this country were able to separate their personal religious beliefs from their desire to create a government that is required to respect individual rights. Our government has legal obligation, it does not have moral obligations. Individuals have moral obligations.
With that said, if our society as a whole does not maintain some level of morality, it is very likely that our Constitution will ultimately fail, as it will also fail if our government fails to uphold its legal obligations.