As far as the actual consequences go...a lot might depend on Japan, because with Britain as part of the Axis, you'd have to think Europe falls under fairly solid Nazi control and Germany is able to focus more on fighting the Soviets, at least assuming that Hitler still decides to double-cross Stalin. Given the political pressures on FDR not to take the U.S. into a "foreign war" and the fact that setting the stage for a D-Day-style invasion would be even more difficult, I'm not sure I see him or any other American President launching a war of European liberation against the Nazis. However, if Japan is still set on expanding into the Pacific and attacks the U.S., then presumably that means the U.S. doesn't quit until both Germany and Japan are defeated.
I'm also thinking that this might spell the end, or at least the shrinking, of the British Commonwealth. Would Canada, Australia, and New Zealand -whatever their ties to the mother country - really tolerate having their people and resources pulled into the Nazi war effort?