Trying to understand the interplay of religion and public life in the United States? A great place to start would be this address by Wilfred McClay at the recent Pew Forum.

An excerpt:

So let me begin with two propositions. The first one is that in the American experience, the separation of church and state, which by and large we acknowledge as a rough-and-ready principle, does not necessarily mean the separation of religion from public life. Another way of saying this is that America has a strong commitment to secularism, but it is secularism of a particular kind, understood in a particular way.

Second, that the United States has achieved in practice what seemed impossible in theory: a reconciliation of religion with modernity, in contrast, as I say, to the Western European pattern. In the United States religious belief has proven amazingly persistent even as the culture has been more and more willing to embrace enthusiastically all or most of the scientific and technological agenda of modernity. Sometimes the two reinforce one another. Sometimes they clash with one another, but the American culture has found room for both to be present. I won't prophesy this will always be the case, but it's a very solid relationship of long standing.

And perhaps I should add-and I did this for my Turkish audiences
[he had recently been on a speaking tour of Turkey]; it utterly baffled them, but it shouldn't be quite so baffling for you-that all this makes sense in light of the fact of [a] third proposition: that American institutions and culture are intrinsically and irreducibly complex-not chaotic, which is of course what they see-but complex.

The complexity takes a particular form: that politics and culture are designed around an interplay of competitive forces, which is, I think, the key to understanding a lot about the United States. The Constitution was based on the assumptions that in any dynamic society there would be contending interest groups, and [that] one could best counteract their influence by systematically playing them off against one another. That was the reasoning behind separation of powers. That was the reasoning behind the federal system. These different parts of the government are supposed to fight with one another. That's how the Constitution is supposed to work.