Salon has a very interesting article on the secular beliefs of early American politicians. It is important for us to understand that the current level of religion in the political domain is fairly recent. We now have an "Islamic Republic" of Iran, Iraq and Afghanistan, where before there was none. We have "In God We Trust" and "One Nation Under God", also fairly recent.
Here's a quote from the article: "In Washington's day, it may have been reasonable for the elite to worry that only fear of hellfire kept the masses from running amok, but in the 21st century it is clear that democracy as a form of government does not require citizens who believe in supernatural religion. Most of the world's stable democracies are in Europe, where the population is largely post-Christian and secular, and in East Asian countries like Japan where the "Judeo-Christian tradition" has never been part of the majority culture."