While I think Diog’s claim is too strong (it could be falsified by even a single instance, despite the prescence of small instances really having very little to do with the issue at hand), I think I can at least provide some useful information on this score.
Let’s start off with Washington.
When a group of clergy complained that the Constitution contained no mention of Christ, Washington replied: “I am persuaded, you will permit me to observe that the path of true piety is so plain as to require but little political direction. To this consideration we ought to ascribe the absence of any regulation, respecting religion, from the Magna-Charta of our country.” – Papers, Presidential Series, 4.274 (1789)
Here’s Adams:
“The United States of America have exhibited, perhaps, the first example of governments erected on the simple principles of nature; and if men are now sufficiently enlightened to disabuse themselves of artifice, imposture, hypocrisy, and superstition, they will consider this event as an era in their history. Although the detail of the formation of the American governments is at present little known or regarded either in Europe or in America, it may hereafter become an object of curiosity. It will never be pretended that any persons employed in that service had interviews with the gods, or were in any degree under the influence of Heaven, more than those at work upon ships or houses, or laboring in merchandise or agriculture; it will forever be acknowledged that these governments were contrived merely by the use of reason and the senses.” --A Defence of the Constitutions of Government of the United States of America (1787)
And of course, the obligatory Treaty of Tripoli, approved by Congress and signed by Adams:
"As the government of the United States is not, in any sense, founded on the Christian religion; as it has in itself no character of enmity against the laws, religion or tranquility of Musselmen [Muslims] … it is declared … that no pretext arising from religious opinion shall ever product an interruption of the harmony existing between the two countries…
“The United States is not a Christian nation any more than it is a Jewish or a Mohammedan nation.”
from the Treaty of Tripoli (1797)
Note that the Senate that signed this into law was almost assuredly more devoutly and old-timey religious than the Senate is today. Yet these Senators had no problem with the idea that there is a difference between the rationalist ideas of political government and the religious practices of a people. Many people seem to have this problem today.
Now for Madison:
“And I have no doubt that every new example will succeed, as every past one has done, in shewing that religion & Govt will both exist in greater purity, the less they are mixed together.” James Madison, letter to Edward Livingston on July 10, 1822
“Who does not see that the same authority which can establish Christianity in exclusion of all other religions may establish, with the same ease, any particular sect of Christians in exclusion of all other sects? That the same authority which can force a citizen to contribute threepence only of his property for the support of any one establishment may force him to conform to any other establishment in all cases whatsoever?” Madison, from “A Memorial and Remonstrance Against Religious Assessments”
Frankly, the idea that Christianity played an important part of forming the Constitution is just silly on the face of it. The point of drafting the Constitution was not to rule on any particular religious matter, it was to create a legal framework on which the nation could more effectively function. It was practical, political, and pragmatic: what was on people’s mind was no more particularly religious in function than is what on most people’s minds, even those people who are very religous, when they try to do some practical task requiring planning and consideration. Indeed, what was remarked upon afterwards: what was considered notable, was how LITTLE influence religion had upon the new government, not how much.
