Logistics decree that the odds of either side defeating the other were slim to nonexistant.
Trying to logistically support forces across the atlantic without some "safe" landing ground is impossible.
If the US had some sort of ally in europe, who the soviets couldn't immediately run over then perhaps, but its doubtful.
Likewise, if the Soviets had some sort of ally in the America's, who the US couldn't immediately run over.
But in both instances, there would need to be a good year or two of building up before hand and most likely it simply would not have been possible. (Consider all the logistical build up for D-day)
Most likely, they would have simply faced too great odds due to the "home" advantage of which ever was attacked. They would have man power, food, ammunition, petrol.. wheras the attacker would have to wait for it to be moved half way around the world.