The debate over whether the US Constitution contains the "separation of church and state" concept was clarified by none other than Rush Limbaugh during a recent radio monologue. What the left and liberals understand by the term is much different from what conservatives and the founding father mean by the the phrase.
Basically the term, like many, has been co-opted by the left to mean the public square should be a religion free zone. That of course would have been anathema to the founders. They understood it mean the separation of religious and governmental institutions not exclusion of faith grounded beliefs and values from the public square. (Frankly, what public views aren't ultimately grounded in faith, faith in God, faith in evolution, faith in materialism, etc. But that's worthy of discussion another time.)