The Public Religion Research Institute (PRRI) researches a lot of different issues at the intersection of religion, values and public life. They are nonprofit and nonpartisan. They conduct polls which have been interesting in the past.
Here is a review of one from the other day:
Their summary paragraph: "The growth of the religiously unaffiliated, who now account for roughly 1-in-5 Americans, may presage warmer feelings toward atheists. Yet what seems more likely, at least in the short term, is that views of the non-religious will improve. Few Americans who are religiously unaffiliated actually identify as atheist. Among the unaffiliated, 3-in-10 (30 percent) are unattached believers, nearly 4-in-10 (38 percent) are seculars, while roughly one-third (31 percent) are atheist or agnostic."
Here is another resource. The Institute for the Study of Secularism in Society and Culture
This is where you can get ARIS (American Religious Identification Survey) research.
They don't do it very often, but these are very interesting reports when they come out.
If you have other resources for secularism or the separation of church and state, please share it with us and we'll pass it on.