Harsh, guy.
By that point in the war, the United States could've done whatever it liked. Obviously, there was still a second nuke chilling in the Pacific, ready to go, and more on the way, eventually. The conventional bombing campaign could've continued till there were no Japanese cities left--after all, nuclear weapons weren't the only way the US was destroying cities in Japan. The US could have invaded, though why, at that point, they would have is beyond me. The US could have accepted Japaneses attempts at surrendering with the caveat that Emperor Hirohito would not be prosecuted for war crimes (which is what ended up happening anyway). The US literally could have blockaded Japan until everyone starved to death, though this probably would've taken some time and been unpopular with a war-weary public (not to mention the negative image evoked by starving a country to death).
So, ultimately, not a lot different happens. Japan loses, almost assuredly in 1945, the second nuke makes the impression on the Soviets anyway and some random guy's mom isn't remembered for all time as the chick whose name was on the plane that nuked Hiroshima.