We have have Sir Edward Coke, and William Blackstone's definition of laws and the interpretation of these laws on how they were applied to the founding of our nation by James Kent, that our laws are firmly built off judeo-christian beliefs.
As far as I know, and being one who specifically studies British law in my leisure, there is little to no historical documentation to disprove this. So if I must address this in a different way to appease the mob, then perhaps I can say that the federal government was founded as a central institution to provide equal representation, to regulate trade, taxation, to ensure coexistence and equality amongst the states, and to provide protection to these states both in peace and at war. (This is all found in the federalist papers)
The absence of wording God into this does not mean that our nation was not a Christian nation, it just simply means that it is not in the federal governments power or interest to regulate or dictate religion of the people it represents. This responsibility along with every other social issue is regulated, defined, or protected by the states.
In a Republic/Democracy a government is defined by its people and it's people are represented by their constitution and their laws. Our laws being built of judeo-christian British laws in fact make our nation at this time a Christian nation and if you wish to dispute this then I suggest you look into reading some of James Kents "Commentaries On American Law" but I firmly believe that if one looks into the laws and into the constitutions of both the federal and state Governments that the conclusion is quite simple to make. The reason I believe that this is ignored or rewritten in today's society is because this simple historical truth brings shame to our more modern secular beliefs on the institution of government