The US was built on 'common sense values'. Be kind, be generous, work hard, take care of your family etc.
The notion of Judeo-Christian ethics stems from the work of George Orwell in the late 30s. He's not American, and that was about 160yrs after the independence.
It still took 10 years or so to finalize a common ground between both sets of moral values, which anyway, are far from being shared only by Jews and Christians.