The US legal history goes back further than the founding fathers. I guess it's safe to assume that the Statute of Anne had a major influence on US copyright legislation (according to Wikipedia, they copied it almost verbatim). I'm neither a lawyer nor a law student, but I think we can view British and US copyright law as one legal tradition then, which started with the early printer monopolies of the 16th century.
Also note that the US constitution doesn't mention the term "copyright" and is pretty vague about the rights that are secured to authors and inventors, and under which provisions. So the constitution doesn't tell us much about the reality of copyright protection.