See John Fea for the obit. Bellah was, in our time, the most noted scholar of the concept of "civil religion" in America. Here is an actual, rather lengthy piece from Bellah on the topic. A taste:
The Idea of a Civil Religion
The phrase "civil religion" is, of course, Rousseau's. In chapter 8, book 4 of The Social Contract, he outlines the simple dogmas of the civil religion: the existence of God, the life to come, the reward of virtue and the punishment of vice, and the exclusion of religious intolerance. All other religious opinions are outside the cognizance of the state and may be freely held by citizens. While the phrase "civil religion" was not used, to the best of my knowledge, by the founding fathers, and I am certainly not arguing for the particular influence of Rousseau, it is clear that similar ideas, as part of the cultural climate of the late eighteenth century, were to be found among the Americans. For example, Benjamin Franklin writes in his autobiography,
"I never was without some religious principles. I never doubted, for instance, the existence of the Deity; that he made the world and govern'd it by his Providence; that the most acceptable service of God was the doing of good to men; that our souls are immortal; and that all crime will be punished, and virtue rewarded either here or hereafter. These I esteemed the essentials of every religion; and, being to be found in all the religions we had in our country, I respected them all, tho' with different degrees of respect, as I found them more or less mix'd with other articles, which, without any tendency to inspire, promote or confirm morality, serv'd principally do divide us, and make us unfriendly to one another."