Honestly I cannot picture that. Just the logistical effort to mount an invasion as a minimum the size of Normandy 44 in France would have been several times bigger. You also have to take in account that no axis power ever intended to invade North America, although Japan technically did it occupying some Aleutian Islands. Both Germany and Japan seeked spheres of influence in their regions and create some puppet states but never invade so much. Even Germany did not intend to invade half of Europe and North Africa as it did once the Pandora box was open. It was pushed by the events, for instance Italians failing to do their bit.