Some of the founders, such as Benjamin Franklin, subscribed to 18th-century Deism: a watery, undemanding doctrine that postulated a Creator who wound up the universe like a clock and thereafter did not intervene in the human story. It has been said that the Deist God is like a rich aunt in Australia: benevolent, distant, and infrequently heard from. Deism seeks to explain the existence and nature of the universe. But so does the Big Bang theory, which is not a religion. If a religion is supposed to console and enjoin as well as explain, Deism hardly counts as a religion.
George Washington famously would not kneel to pray. And when his pastor rebuked him for setting a bad example by leaving services before communion, Washington mended his ways in his characteristically austere manner: He stayed away from church on communion Sundays. He acknowledged Christianity's "benign influence" on society, but no ministers were present and no prayers were said when he died a stoic's death. This, even though Washington had proclaimed in his famous Farewell Address (which to this day is read aloud in Congress every year on his birthday) that "religion and morality are indispensable supports" for "political prosperity." He said, "Let us with caution indulge the supposition that morality can be maintained without religion." He warned that "reason and experience both forbid us to expect that national morality can prevail in exclusion of religious principle."
The longer John Adams lived, the shorter grew his creed, which in the end was Unitarianism. Thomas Jefferson wrote ringing words about the Creator who endowed us with rights, but Jefferson was a placid utilitarian when he urged a nephew to inquire into the veracity of Christianity, saying laconically: "If it ends in a belief that there is no God, you will find incitements to virtue in the comforts and pleasantness you feel in its exercise, and the love of others which it will procure you."
James Madison, always commonsensical, explained — actually, explained away — religion as an innate appetite: "[T]he mind prefers at once the idea of a self-existing cause to that of an infinite series of cause and effect." When the first Congress hired a chaplain, Madison said "it was not with my approbation."
Yet even the founders who were unbelievers considered it a civic duty — a public service — to be observant unbelievers. For example, two days after Jefferson wrote his famous letter endorsing a "wall of separation" between church and state, he attended, as he and other government officials often would, church services held in the chamber of the House of Representatives. Services were also held in the Treasury building.
Jefferson and other founders made statesmanlike accommodation of the public's strong preference, which then as now was for religion to enjoy ample space in the public square. They understood that Christianity, particularly in its post-Reformation ferments, fostered attitudes and aptitudes associated with, and useful to, popular government. Protestantism's emphasis on the individual's direct, unmediated relationship with God and the primacy of individual conscience and choice subverted conventions of hierarchical societies in which deference was expected from the many toward the few.
Beyond that, however, the American founding owed much more to John Locke than to Jesus. ...I think Will -- like a lot of folks -- doesn't quite get Franklin who was more theistic than deistic. Likewise, "Unitarianism" wasn't just John Adams' ending creed; it was the creed he held for his entire adult life.