At ScienceBlogs I look at World Values Survey data and compare secular and conservative East Asian nations to the religious but liberal United States. I conclude (after looking over data tables):
My point here is rather simple: increased secularism in the United States would almost certainly lead toward a shift to greater Left-Liberalism. But that dynamic will almost certainly exhibit diminishing returns as secularization proceeds and the personality and social profiles of atheists starts to converge upon the general population. The bad news for conservatives is that I think the secularizing tendency in America during the current period is good for liberalism. The good news is that it probably isn’t as bad as it could be if you extrapolated on a straight line from the current secular population in terms of political outlook.