there is no law requiring you to carry ID at all times.
you are required by law and regulation to bear a drivers license at all times when driving, but if youre walking your dog, going to the corner shop, riding public transit or bicycling you are not required to possess ID at all.
to do many things, like cash a check, board a plane, rent a hotel room, rent a car (duh) request a loan from a bank, or any of a variety of other things you are required to prove your identity, but you are otherwise NOT required to carry ID.
there are several state laws which require that if a cop asks for ID you must present it, but if you do not have any ID on you, you cannot be compelled to present what you do not posses.
there are also several states which require that when a cop asks who you are you MUST identify yourself, but there is still no requirement to have ID
the few states which have attempted to create a mandatory ID law have had their proposals shot down on constitutional grounds, usually before they get out of committee, and there is no federal law requiring ID.