Today many evangelicals, Baptists in particular, would love to see explicit references to God in the Constitution of the United States. This desire is completely at odds with that of Baptists of the early days of this country. When the Constitution was proposed in 1787, Baptists opposed it because it contained no explicit guarantee of religious liberty. The document contained no reference to God at all, but that did not bother Baptists. Indeed, they preferred it that way.
Baptist minister and leader John Leland led the Baptist charge for the addition of a Bill of Rights to the Constitution, including the guarantee of religious liberty for all. But Leland and his fellow Baptists wished the Constitution to remain "Godless." Later Leland pressed a revision to the Massachusetts state Constitution. One item in that document that Leland and his fellow Baptist opposed was the assertion that "it is the right and duty of all men publicly, and at stated seasons, to worship the Supreme Being." Leland wrote in 1794 that he agreed with the statement but he and his fellow Baptists maintained that it "would read much better in a catechism than in a state constitution."
Baptists of earlier days preferred "Godless" government Constitutions because they were firm advocates of the complete separation of church and state. Virginia Baptists suffered severe persecution at the hands of fellow Christians in the government sponsored Anglican Church from about 1760-1780. This ugly example of the mingling of church and state taught Baptists that the two should be kept separate.
And so "Godless" government Constitutions were just fine with Baptists of the late 1700's and early 1800's. Would that this were still true today.