I had a theory slightly different: what if the US and Nazi Germany never fought?
After Japan attacks Pearl Harbor the US declares war on Japan. But instead of Germany declaring War on the US, Hitlers staff realize its a losing war. The US concentrates on defeating Japan; Germany is focused on Russia and ultimately defeats them.
The US only mildly supports England, but many in the US wanted to see the breakup of the British Empire (This was actually one of the caveats of the Bretton Woods discussions in 1944). Germany ultimately forces England into defeat and destroys the British Empire, making England a puppet state, lets say under Oswald Mosley. In the east China becomes an uneasy US ally in the fight against Japan and together the US and China defeat Japan.
By 1962 there are three spheres of influence in the world: Nazism which stretches from the coast of France to the Urals, through north Africa and the middle East; Capitalism lead by the US in the Western Hemisphere and Communism led by China in the East.
A sort of Cold War has emerged between the three powers: The US has economic might, the Nazi State has military might and the Communist China state has technology, although through uneasy trade alliances each power has access to portions of the other.