Seems like your arguing two separate ideas. Please correct me if I'm wrong, and I in no way mean that sarcastically, but proclaiming Christianity as a political tactic while simultaneously fearing the nation be a Christian nation seem contrary. Most of the people at that time were equally fearful of the country controlling their freedom, especially through religion. How does it help politically to claim the very thing they fled England from unless it be true. And I am very aware the Jefferson thought the miracles in the New Testament were fiction, yet he proclaimed Christianity as...
God who gave us life gave us liberty. Can the liberties of a nation be secure when we have removed a conviction that these liberties are the gift of God? Indeed I tremble for my country when I reflect that God is just, that His justice cannot sleep forever.
– Thomas Jefferson, Jefferson Memorial
Again I never said America was or is a Christian nation, but that the structure of early America was greatly influenced by the Hebrew people. Until 20 years ago this was taught in schools across the US.