As Sir Lion suggested I have not given any sort of debate-worthy material. I guess here it goes.
I think the real essence of what we are trying to get at, with the question "Was the United States founded on Christian principles", needs to be broken down into smaller questions.
1) What are Christian Principles?
2) What principles of Christianity are exclusive to and only to Christianity.
3) Is the United States based the expressed principles of the founding fathers, or what they considered their principles in a more personal life.
I think we need to make this a little bit simpler and consider that by "Principles" we are talking about "Morality". Basically, whether the idea of America's Morality is the same as the idea of Christian Morality. Furthermore, we would also have to ratify that America's Morality is exclusively the morality of Christian doctrine, and not a universal morality.
We need to see what the thinkers for contemporary moral philosophy have to say about it. David Hume, and Emmanuel Kant.
Hume was an empiricist; to believe that all knowledge is gained through experience.
Plan and simply, his views on Morality would be that morality follow from the self like so:
Experiences bombard the senses. Each experience is different for each individual. Out of the experiences we create the concept of morality, therefore there is no universal morality as each experience is different and knowledge cultivates morality. This philosophy also indoctrinates the idea that no one is punishable for wrongdoing, as morality is different based on each individual. Now I am on board with saying this one is not how America does things, as we throw people in jail for even the pettiest of crimes.
Emmanuel Kant was a rationalist. He fused ideas that the human knowledge is gained from both physical and metaphysical realms (experience and a categorical interpretation of the experience.)
Kant believed that morality is ""Act in such a way that you treat humanity, whether in your own person or in the person of another, always at the same time as an end and never simply as a means." which looks very similar to Christianity's golden rule (Kant was an agnostic, I could explain this point as well if you want me to).
What does this mean?
Well I think that more American legislation and laws are in the good will of this doctrine; this Universal law (as it is found in at least 21 religions around the world:
Versions of the Golden Rule in 21 world religions) is not a creation or an explicit Christian idea-- it spans ideas from all over the world from different cultures.
This is very basic summation, if I need to go more indepth then I will.
Basically,
No, America is not founded on Christian principles because the principles on which America is founded on (Ethics of Reciprocity) are not exclusive to Christianity.