I'm constantly amazed at the veneration that Americans give to a bunch of 250 year-old politicians. 250 years ago, we British 1) allowed slavery, 2) had the death penaly for theft 3) burned witches. We think that we've come a long way since then, and mostly we don't subscribe to the views of 250 years ago.
Yet an almost religious fervour is given to the founding fathers - no, I'm wrong, it *is* religious. There's a set of documents that are, it would seem, inerrant. There's a set of people who were, it seems, inspired by revelation and are quoted as authorities in many debates. And although there have been 27 amendments to the US constitution, it's treated as if it were written in stone (while arguments rage about the meanings of the words). Just like a religion.
It's actually easy. All you have to do is decide amongst yourselves what your laws should be, and enact them. If you want to be a Christian Nation, then you can be, and good luck with that, although the word "Christian" includes many groups (are the Mormons Christian? Scientologists?) and you may have trouble defining what is meant. If you want to be a secular nation, with people's religions their own business, then good luck with that too (and we Europeans would prefer that, we have enough refugees right now without more pouring across the Atlantic).
My guess is that, if a vote were taken, Americans wwould vote for "secular". But that's just a guess from a non-American.