For one thing you probably would have had something resembling a mutiny among tens of thousands of GIs who were very tired of war by that time. The idea of initiating a major new war against our erstwhile Russian ‘ally’ on the heels of defeating Germany is a thought peculiar to Americans far removed those times. Patton was given to hyperbole and short of the Soviets invading the western sectors nothing was going to happen. The Soviets had a massive battle hardened army with internal lines of supply. It’s not hard to figure out how long and bloody that fight would have been.
And that's not even the half of it.
What did you think, a war is a walk in the park?
That armies can just ramble around, wandering hither & yon, like Hitler in Russia, and expect to win anything?
Do you imagine that America had an infinite supply of not only war materials, but also endless enthusiasm to go sacrificing millions of our own boys deep in the heart of Eur-Asia?
And for what?
When had "Uncle Joe" ever attacked us?
For that matter, if you believed the "mainstream media" of the day, wasn't Russia some sort of socialist democracy, sort of like heaven on earth?
Why would we want to fight those people?
The simple fact is that, short of some kind of direct attack on us, there was no way the American people were going to support yet another war, and against the very folks who had just sacrificed so much to help us win The Big One.
So Patton, God bless him, could bluster all he wanted to, but Americans were not going to kill one Russian who did not shoot at us first.
That's a simple fact.