That's rich considering it was France and the UK that threw Poland under the bus despite having a signed defense pact. The US just came in to clean up the mess.
Churchil wanted to pressure Stalin to leave Poland (and at least parts of EE) independent and even considered "Operation Unthinkable".
At least that's what I think the guy above referenced.
"Bluff" because no one other than perhaps Stalin would have followed through—to essentially extend WWII (this time between former allies).
So pragmatism was the order of the day, thus Poland and EE were sacrificed.