MHorton has put it well, but I can’t resist making a few adjustments. The Framers comprised a variety of “Rational Christians,” primarily Baptists, who were adamantly opposed to any attempt to link church and state. With the Deists and Unitarians they represented the Enlightenment mind set that MHorton describes . Let me add a few specifics for clarity.
From Roger Williams, patriarch of the Baptist faith:
"It is the will and command of God that, since the coming of His Son, the Lord Jesus, a permission of the most Paganish, Jewish, Turkish or anti-Christian consciences be granted to all men...God requireth not an uniformity of religion to be enacted and enforced in any civil state...An enforced uniformity of religion throughout a nation or civil state confounds the civil and religious, denies the principles of Christianity and civility, and that Jesus Christ is come in the flesh."
From Thomas Jefferson (in a lletter to William Short):
"But the greatest of all reformers of the depraved religion of his own country, was Jesus of Nazareth. Abstracting what is really his own from the rubbish in which it is buried, easily distinguished by its lustre from the dross of his biographers, and as separable from that as the diamond from the dunghill, we have the outlines of a system of the most sublime morality which has ever fallen from the lips of man."
In a footnote appended to this letter, Jefferson identified that to which he referred to as rubbish thus:
"The immaculate conception of Jesus, his deification, the creation of the world by him, his miraculous powers, his resurrection and visible ascension, his corporeal presence in the Eucharist, the Trinity, original sin, atonement, regeneration, election, orders of the Hierarchy, etc."
From Benjamin Franklin (when pressed about his religious convictions):
"You desire to know something of my Religion. It is the first time I have been questioned upon it. But I cannot take your curiosity amiss, and shall endeavor in a few Words to gratify it. Here is my creed. I believe in one God, Creator of the Universe. That he governs it by his Providence. That he ought to be worshipped. That the most acceptable Service we render to him is doing good to his other Children. That the soul of Man is immortal, and will be treated with justice in another Life respecting its Conduct in this. These I take to be the fundamental Principles of all sound Religion, and I regard them as you do in whatever Sect I meet with them."
Now we come to Franklin's thoughts about Jesus.
"As to Jesus of Nazareth, my Opinion of whom you particularly desire. I think the System of Morals and his Religion, as he left them to us, the best the World ever saw or is likely to see; but I apprehend it has received various corrupting Changes, and I have, with most of the present dissenters in England some Doubts as to his Divinity; tho' it is a question I do not dogmatize upon, having never studied it, and think it needless to busy myself with it now, when I expect soon an Opportunity of knowing the Truth with less Trouble. I see no harm, however, in its being believed, if that Belief has the good Consequence, as probably it has, of making his Doctrines respected and better observed; especially as I do not perceive, that the Supreme takes it amiss, by distinguishing the Unbelievers in his Government of the World with any peculiar marks of displeasure."
Prayerat the Constitutional Convention:
"It is perhaps symbolic of the difference in the relationship of state and religion between the Continental Congress and the new government established by the Constitutional Convention of 1787, that whereas the Continental Congress instituted the practice of daily prayers immediately on first convening, the Convention met for four months without any recitation of prayers. After the Convention had been in session for a month, the octogenarian Franklin, who in earlier years had been pretty much of a Deist, moved 'that henceforth prayers imploring the assistance of Heaven, and its blessings on our deliberations, be held in this Assembly every morning before we proceed to business, and that one or more of the Clergy of this City be requested to officiate in that service.' The motion was received politely though not without embarrassment. According to the records of the Convention, 'After several unsuccessful attempts for silently postponing the matter by adjourning, the adjournment was at length carried, without any vote on the motion!".
No formal prayers were ever recited at the Constitutional Convention.
What’s in the Constitution? Most people are familiar with the so-called “freedom of religion” statement in the Bill of Rights. Fewer are familiar with Article VI, Section III, which specifically prohits any religious test as a condition for holding public office.
The elimination of religious tests for public office by the Constitutional Convention of 1787 represented a major achievement for the future course of American church-state relations. Article VI not only removed the basis for any preferential treatment of one religion over another for holding public office, but also denied the right of any preferential status of religion over nonreligion in matters of one's political participation in the life of the Republic. William Lee Miller appropriately noted in his recent historical review of religion and the Constitution, The First Liberty: Religion and the American Republic, that "in the framing of Article VI ...the new nation was electing to be nonreligious in its civil life." On the subject of religion, Miller finds "more striking than what the Federal Constitution did include is what it did not." Unlike other legal documents of the period and throughout history, there art no references in the Constitution to the Deity, to God, to "Providence." or even to the Creator, as in the case of the Declaration of Independence, which, unlike the Constitution, was not a formal legal document.
Shortly after its founding the US became embroiled with the state of Tripoli over the issue of piracy. The conflict was resloved in 1796, and the treaty bringing it to a close contains the following passage:
Article 11 read, "As the govemment of the United States of America is not founded in any sense on the Christian religion - as it has in itself no character of enmity against the laws, religion or tranquility of Musselmen [Muslims] - and as the said states have never entered into any war or act of hostility against any Mahometan nation, it is declared by the parties, that no pretext arising from religious opinions shall ever produce an interruption of the harmony existing between the two countries."
In the Senate, the treaty barely caused a ripple. According to The Journal of the Executive Proceedings of the United States Senate, the treaty was read aloud on the floor of the Senate and copies were printed for the senators. No discussion or argument about the document was recorded, and the vote in favor was unanimous. It was also reprinted widely in newspapers, and there is no record of public objection to its wording.