The western allies wouldn't need to throw millions of (their own) men into the meatgrinder. Unless you butterfly away the Manhattan Project, they won't have any problems nuking Germany.If we assume ridiculously successful Case Blue, followed by Moscow 42, and Stalin's government falls resulting in a small rump Soviet union east of the Urals, I don't think that the US and the UK have the will to go the distance. They'd likely take North Africa and maybe Sicily, stomp Japan into the ground, but I don't think they'd be willing to accept the casualties required to take back Europe.
The US and the UK COULD do it. I just don't think they would. The US suffered on the order of 400k killed in WW2. I doubt its casualty budget extends into the millions.