It was a Supreme Court Ruling (Sony Betamax) that user controlled copies are not a copyright violation. I doubt that Congress would work to work around that decision.
They sure could. All they have to do is allow ota broadcasters to encrypt their signal. And since breaking drm is illegal, there's your answer. Now would congress pass a law like that? In today's environment where the FCC wants to take away even more ota bandwith, it's possible.