Hey, first post here so I hope i dont bring down anyones wrath. And do forgive spelling mistakes :? Just try not to shoot me down too badly ok
As usual, the answer is always more grey than black and white, but IMHO I believe the US would have most definately lost, and badly, if the war was fought on russian soil.
Size of forces aside, the USSR had, in the 30's been at the fore front of mechanized developement and were already developing the weapons and resources which aided them in winning vs the Werhmacht. Their developement of mechanized tactics were also ahead of most nations.
Fair enough that Stalin had a fit and the mechanized elements of the red army were put on the back burner just prior to Barbarossa, we've seen how quickly that was remedied and the formation of tank armies became the norm.
The massive human and materail resources available to the USSR would also be a deciding factor, as the black soil regions and caucasus oilfields were not threatened by Germany and were totally available for the ruthless mobilisation we have all learnt about.
Sorry i cant give too many examples, no access to my library at the moment
"If they were to have a war it would most definetly be fought in Alaska. And at the time they would have taken most of Alaska due to the fact we had little ways in means of transportation to get there, but the American people would mobilize and would most likely force USSR out of Alaska and force them to a peace treaty."
Soviet ability in winter fighting, would tip the balance infavour of USSR here I believe. The US would mobilise, yes though i do still think the USSR would have the numbers in the end. I'm not sure how effectively each would resupply due to natural obstacles for both sides.