So, In response to the question posed above, I feel that we need to set a few ground rules first, and to try and clarify a few things.
1.) Should it possible? absolutely. From both a game, and real life POV, anything can happen.
2.) Should it be very difficult? well, yes. You are invading a massive nation that has substantial infrastructure and economy, and enough paranoia to be prepared. They were also comparatively less ravaged by the wars attrition, and would have more oomph to bring to the front, so it would be difficult.
With that out of the way, onto some points that I feel may need clarification.
1.) so we can assume that we are talking about if the axis wins the war, as it is doubtful the allies would turn on america.
2.) what lands would be taken to assume a "win" in Europe? can we assume that all of Europe from the uk to poland, and from Scandinavia to south Africa would constitute the axis win? does japan take on India after china? what are the defined borders were working with?
3.) what would be the invasions time frame? would the axis immediately just go for it? or would they have a period of time to replenish, rebuild and renovate? If we can assume a longer time period, then what effect would this have on the US economy? such that, how would their trade be effected if the vast majority of their nearby neighbors are effectively embargoing them? would they still have sufficient funds if they cant trade with many of the major nations?
4.) would they have already dealt with the soviets?
So, imagine/ assume, that the axis is gearing for an invasion. They control europe, and have been using their time to re arm and reasses the situation. I see a few invasion routes they can take.
1.) hit up the fascist states in south america,do them a solid and help them take over the other states. This would give a good southern invasion route, and since they would control africa they can use that to help them move supplies, forcing the US to spread their navy between the pacific and Atlantic coasts, and forcing them to cover both north and south america if they wish to intercept as many fleets as they can. This can gain more potential if they manage to do something like capture the Panama canal, and close it to american shipping. The axis would however run into issues with infrastructure to move a massive army, and the fact that the border there is effectively rather small(in comparison to CA-US) and could lead to a bit of bottlenecking, all the while the axis might not have sufficient airfields to terrain to maneuver tanks and aircraft to counter the US.
2.) Straight assault. The riskiest, as it would be effectively the reverse D-day. I dont think I need to mention more on this, other than it would be a logistical nightmare and a massive expenditure
3.) I would say the most likely choice would be to head on over to Canada. Assuming that the UK has fallen, Canada has lost its 'parent' and has been forced to start trying to regather itself effectively on its own. It is the most likely target for many reasons.
A.) Newfoundland is the closest place to Europe in north america, and was also home to the largest airfield in the world at the Time. Gander airport was built to be an effective refueling station for trans Atlantic flights, and as such would hold significant strategic importance for any nation to hold, as it would allow the holder to move planes and supplies by air to the front.
B.) We also have evidence that the germans were already scouting the island during the war, what with the submarine found off the coast and such(I do believe its in a museum in Ontario now). With its low population, little infrastructure, and minimal military for resistance it would provide an optimal place to stage a north american invasion, especially if the axis has already taken greenland and iceland, so as to remove long and risky trips.
C.) From here, the maritimes could be taken ,and the axis could press westward, allowing them to open a massive front line along the (CA-US) border. This would allow them to press in from the middle of the nation and separate it, or to sweep into the west to relieve the Japanese, and then use that to help them push east.
D.) It doesn't help that much of Canada population, and a significant amount of infrastructure and industry is concentrated along the border.
It is certainly possible that it could have happened. No nation is impregnable or invincible, and even america would eventually fall if the axis could gather their strength against it.
