Germany did not have the sealift to perform more than a raid, and had no ability to re-supply across a beach. Translation = epic fail.

Moreover, even if they had had the sealift, they would also have had to radically increase the size of their naval forces at all levels. No European power had the economic strength to build such a fleet, and certainly not Germany. Remember, this is the English Channel and THE homeland. The Home fleet's sole purpose was to defend that, even at the cost of all units and personnel. No naval force existed that could have successfully screened such an invasion force against an all-out effort by the RN prior to the advent of the 1944 US Pacific Fleet.

The Soviets probably WOULD have attacked had Germany committed to an invasion of Britain, but it would have been a limited assault for purposes of acquiring Rumania and some of the other Balkan territories. It has been theorized that part of the "too far forward" deployment that the Germans exploited during Barbarossa was because Stalin was hoping for an opportunity to do just that.