A coworker, who is a history buff, says that the US was founded on Christian principles. He states that opponents of the claim that it was not often point to Ben Franklin and Thomas Jefferson, but fail to look at the other founders.
I don't think the question is well formulated. Define "founded on" and also "Christian principles". Which principles are referred to, and what is the sense in which a nation can be founded on them? What does it mean for a nation to be founded on a principle in the first place?
To put it differently, if the US were founded on Christian principles, how would you tell? What kind of evidence would you look for?
This is the type of question that will get different answers, and each answer will quote sources. So good luck trying to get to the bottom of this. But, with everything else, remember that the US (or, colonial America) was quite religious. One estimate is that in the early 1700s, 75-80% of people attended church. So, while some of the founders were not Christian, the majority of the people they interacted with in their communities were Christians. For example, Benjamin Franklin was not a Christian, but his mother was. Though, while Franklin was not a Christian, he believed that what Jesus' "system of morals and his religion, as he left them to us, the best the world ever saw or is likely to see". This is from a letter to Ezra Styles. Read the rest of the letter (it's very short), and you'll see that while he's not a Christian, he's certainly nowhere near being any sort of "anti-Christian", and he certainly claimed to be quite familiar with Christian teachings and viewed them positively.
And, I should also point out, at that time there were very few Catholics living in the colonies. So, in the above, Christian = Protestant. While that doesn't mean much to many, I'll point out that there is a very rich history of Protestantism that bears on this answer as well. One example of many on how this bears to your question is that in protestant churches, members elect their own leaders.
So, the country was founded by people who either were Christians or who where raised by Christians, who associated with Christians, and who were living in a community where many of its values, such as self government, were heavily influenced by Christianity.