If Britain had been invaded and occupied, I sincerely doubt the Americans would have been able to invade Europe at all. With German airbases all across Britain, the US would have had a hard time moving any ships near the European coast. D-Day would have been impossible, and with no forces tied up to defend France against such an invasion, the Russian attack might not have gone so well.
Personally, the US joining the war effort was the major turning point - a large influx of men and materiels bolstered the small, flagging British army, providing the sheer numbers necessary to make progress on the Western front. Of course, their initial reluctance to listen to British advice and use of WW1 tactics meant they were a bit of a liability to start with, but by the end they were a most powerful ally - particularly because prior to joining the war they had had several years of getting fat from selling weapons and goods to both sides.
That said, I think I have to agree that Hitler turning on the USSR was a more devastating move for Germany. If he had been able to focus the bulk of his army on the Western front then maybe even American support might not have been enough.
