Xen said:
Maybe there will be a temporary cease fire between the USSR and UK until the common enemy is knocked out. The conflict between Moscow and London would resume during the race to Berlin and re-conquer all of Germany. Im not too sure if the Soviets would try to make peace with Britain being so closely allied to the US, however if Stalin felt threatened its possible, even probable.
Which, for all practical purposes, is exactly what happened, albeit in a slower, non-combat style. We called it the Cold War.
I think the biggest shift in tactics if the Allies (ca. 1939/40) were to lump the USSR in with Germany would be moves against Soviet southwest Asia, as Matt alluded to. Seizing oil-rich areas and Black Sea ports would be of paramount importance, to limit the flow of oil and other materiel to the North African campaign.
Hitler and Stalin would be chafing the whole time, however. Hitler would know he had to launch the Western front at some point, and take the war to France on his terms, rather than wait and be invaded. That would draw troops away from the Northern front, allowing Hitler's Soviet "allies" to seize more and more territory around the Baltic Sea. The Red Army, on the other hand, would be surging out from all sides, once they realize that they can only go so far west, and would be extorting the invasion of France in return for beating back the UK in the south and re-opening shipping lanes into the Med.
I agree that Churchill would be hard-pressed to maintain the war against the USSR once Hitler turns back to the East. BUT...
What if Stalin's the one who breaks the alliance, instead? Say the USSR decides to step farther than Hitler intended in Sweden...or gets fed up with the partition of Poland and decides to claim a bigger share?
There's no way Churchill would seek terms with Hitler, not with France and the Low Countries occupied. But since there is no "victimization" of the USSR, prevailing sentiment continues, and is perhaps further enflamed against Stalin (particularly if the reports/rumors of massacres are public by then).
As a result, the USSR would see no Lend Lease money or materiel from the US, keeping them weak when Hitler counterattacked. Hitler, would, of course, be making overtures to the West for peace...to no avail.