I wholeheartedly agree that we are a "Christian nation," much as India is a "Hindu nation," or Iraq a "Muslim nation;" eg. the majority of our population is Christian, and our social norms and mores are based on Judeo-Christian teachings. Our religious foundation, however, is not codified in the legal documents that form the basis for our government. Yes, the Declaration is a decidedly "God-friendly" document, but it served only to sever the ties with Great Britain, not create a government for the colonies. The Constitution details what "constitutes" our government, and there is no mention of morality or religious beliefs at all. Socially, yes, we are heavily influenced by Judeo-Christian tradition. Legally, we are influenced by Locke, Montesquieu, Rousseau, et al.
As far as the state constitutions go, I would prefer that THEY had more sway than the US Constitution. We are far to federalist for my tastes--California should be able to bask in a secular-humanistic absence of any Western moral teachings, just as Texas should be able to have an Our Father said before every football game. However, state constitutions, while not necessarily in disagreement with the US Constitution, do not hold national power--they only affect a particular state.
We are most certainly NOT a "Christian nation." We are a secular nation formed on Christian principals (BTW the "Judeo" part is superfluous PC nonsense -any "Christian" principal is implicitly "Judeo" as well). There is a HUGE difference. America has always been a Great Experiment in religious freedom. It was founded as such.