Oh, Japan was quite thoroughly enough in the ropes already and by that point the war in Europe was already over. It was just a question of how the heck you could convince the buggers to admit they lost already.

As a funny side note, I once read somewhere the pre-nuke plans the US had for invading the Home Islands also toyed with the idea of massive chemical-warfare saturation of at least the landing areas to clear the way... I'm not sure how true that is, but in any case the sheer potential for mayhem and massive collateral civilian casualties involved would probably make even nuking two cities seem fairly tame in comparision...

I'm under the impression Fat Man and Little Boy had been a bit of a stretch for US resources of the time, though, so if they were to drop a third one it'd probably have taken a while to get the damn thing built in the first place.