Is Our Constitution Godless?

The constitution was, of course, written by individuals who, although I haven't personally researched them, I can assumed were all at least deistic in their beliefs (to them, there was a rational God who did not meddle in the affairs of humans). And, of course, this influence can be seen throughout the constitution, both in direct remarks ("In the year of our lord", etc, etc...) and in the basic principles of fairness set down in the document itself. However, the issue that the founding fathers, and many of the people during this time period, came into contact with, was that regardless of how fiercely they believed something, and how much they pushed others to believe it as well, they would never get anywhere by coercing other people to obey a set of religious rules that they did not agree with, and even when they could that it would be unfair to the person being coerced, and would not be helpful to the coercer. This is where the idea of creating a state without an official religion came about. Our founding fathers were, by and large, Christian, and yet they understood that for a government to work, it would need to be able to respect all religions, regardless of what the leadership of that government felt. So, in a sense, the constitution was a document created by Christian individuals, but specifically attempts not to impose that Christianity on the people in order to keep the state together.