I think Churchill was up for smashing the Russians, as he rightly saw communism as a huge threat to the West. However, Britain and the allies were particularly fed up with the war and could never have been persuaded to go all out. However, I'd say that if push were to come to shove, and we had engaged the Soviet union in all-out war, then we would have won within a year or two. Russia was so reliant on western logistical and intelligence help that the edge would have been ours. Also, the development of the atomic bomb would have given the US the decisive capability to either destroy or coherence Russia into submission.
Interesting scenarios to consider would what would the allies have done with Germany during a war with Russia? Would we have employed the huge reserve of German manpower and expertise we had in POW cages? How would the war with Japan have progressed? According to some historians, Japan did not surrender because of the atomic bomb, but due to the huge Russian armies coming down upon them in the north...