Ahh yes the old 'separate of church and state' chestnut. OK simply, it doesn't exist in the Constitution. Its a part of a handwritten letter from Thomas Jefferson to the Danbury church in 1802. http://www.loc.gov/loc/lcib/9806/danpre.html
All Jefferson meant was that govt couldn't pick favorites. That wall was the prevention of that. Considering he wrote the first amendment, I think he would know. He was a deist. So yes he believed in God. But he didn't want Catholicism crammed down peoples throat.
Its like if Obama wrote a letter on Obamacare and stated that his dog should have been covered, and centries later this letter is being used to justify petcare in the ACA behemeth.