Biggest threat to Germany was Russia and they knew it. Stalin's 5 year plans brought Russia kicking and screaming to the 20th Century and with the help of the previous German government who supplied plans/arms/technology with the Russians, in return the Russian's allowing the German military to secretly train there, the Russian's really did have an advantage.
The fact was, Hitler had to attack Russia as soon as possible, because Time favoured the Russians, however, on that note, Hitler was never in an "optiminal" situation where he could invade Russia and by all accounts, probably did attack Russia at an optiminal moment when he took Stalin by surprise, due to the fact it was illogical for him to do so.
Apart from the whole conspiracy talk where Pearl Harbour was set-up as an excuse for the US to join the war, if the Japanese restarted the Russo-Japanese war instead, it could have really applied pressure to the Russians.
Heading more on-topic, Hilter didn't need to invade Britain, all he had to do was cripple Britain to take them out of the war effort. Eventually enough, Britain would have had to been forced to accept a ceasefire, if not a surrender.
The main catalyticism for America joining the world, however, was the Russians fighting Hitler back, because if they didn't join in, Western Europe as we know it would be a completely different place.
Bookmarks