This is a question that came up in the worldnews thread about Japanese steel workers. Many people argue that the atomic bombs were a necessary alternative to a homeland invasion to force Japanese surrender. However, I've been doing some preliminary research and it seems that many military strategists such as Eisenhower, MacArthur, Leahy, and Nimitz believed that Japanese surrender was inevitable without military intervention due to the destruction of their air force and navy, leaving no offensive capabilities left. As Nimitz said,
"The Japanese were already defeated and ready to surrender because of the effective sea blockade and the successful bombing with conventional weapons."
Why couldn't the US force Japanese surrender through passive military action, especially considering the Soviet invasion? Was it due to the US wanting to occupy Japan before the Soviet Union in preparation for the Cold War?
By the time of the Potsdam Conference there was an explicit desire by top-level American politicians (Truman and Byrnes in particular) to have the war end before the Soviets got involved. That was the motivation behind the timing of the atomic bombs — the first good-weather days after the Potsdam Conference ended, hopefully prior to the Soviet entrance into the war (the Soviets moved up the date after Hiroshima). The US invasion of the Japanese mainland (Operation Downfall) was not planned to start until November 1945.
Separately, it is worth keeping in mind that defeat is not the same thing as surrender. The Japanese were defeated by August 1945 — they could no longer wage war effectively. However they had not surrendered. Their political system was still intact. The question for the Allies was, how do you get from that scenario to one in which the Japanese political system has surrendered? Would one accept a conditional surrender, or must the end be wholly unconditional? Would one want to wait until the Japanese population starved, hoping for a revolt that would be friendly to the Allies? Etc. This is and was a tricky issue, because even a defeated Japan was still a prickly one — it still had control over its homeland and would be a difficult invasion target. The Allies did not want to leave Japan as it was, in the same political circumstances that originally led to the war.
So one has to distinguish between statements about the militarily defeated nature of Japan, and the question of their acceptance of the end of the war and the terms. The Japanese high command was not willing to accept unconditional surrender in early August 1945, and even when they did surrender (after the atomic bombs, after the Soviet invasion) they attempted to attach some conditions about the state of the Emperor, before finally agreeing to accept whatever the Allies had in mind. (And the Allies did, in the end, allow the Japanese Emperor system to remain in a symbolic form.)
A good source on the final weeks of the war from the American, Japanese, and Soviet points of view is Hasegawa's Racing the Enemy.