The difference between Denmark and the US is that the US would
never implement cycle infrastructure that could possibly increase travel times for cars. Denmark is willing to reduce the convenience of roads for motor vehicles, and that makes for a vastly better cycling experience. (Actually, cycling is fine in the US, but you have to be brave when you are just starting out. Copenhagen has designed in features that makes the roads very newbie-cyclist-friendly, so people don't get scared off the first time they ride on the street.)
Anyway, if the US ever wants to see cycling adopted by the average person and not only people who have already made the decision to commit, we need to: reduce the speed-limit in city centers to 20mph; have bicycle-only light timings; and start selling bicycles that are useful, not just "cool looking".
My guess is that this will not happen in my lifetime.