The US land invasion of Kyushu (the southernmost of the Japanese home islands) was planned for November 1945. (The invasion of the main Japanese home island, Honshu, was planned for the spring of 1946, but had not yet been authorized by Truman.) Even without the atomic bombings, a major event that would have occurred between August 1945 and then would have been the Soviet declaration of war and invasion of Manchuria. It is clear from the Japanese archives that this had a huge effect on their willingness to continue the war, arguably at least as much, if not more, than the news of the atomic bomb being used. In fact, there is evidence that Japanese military planners were assuming that war would be declared by the Soviets in the fall of 1945, and that this would give the Japanese an opportunity to perhaps play the Soviets and Americans off of one another (for the Japanese correctly realized their alliance was relatively tentative by that point) to negotiate for a surrender to one country or the other.

Now it should be noted that a) war planning takes into account many possible options, and is not a reflection of what actually might happen, and b) that the Japanese high command was hardly unanimous about its feelings about the prosecution of the war, but combining the above with the fact that, even by the summer of 1945, there were some in the high command, with the blessing of the Emperor, seeking a "diplomatic" end to the war and doubting it could go on, and the fact that the blockade of Japan meant that it was likely to soon suffer a crushing famine, it seems rather unlikely the war would have continued even until November 1945 (the Kyushu invasion), certainly not to Spring 1946 (the larger Honshu invasion). But this is, of course, speculative.

This view is not just a modern, revisionist, leftist, whatever perspective — it was what the US military found in July 1946 when they studied the issue. The US Strategic Bombing Survey for the Pacific concludes:

Based on a detailed investigation of all the facts, and supported by the testimony of the surviving Japanese leaders involved, it is the Survey's opinion that certainly prior to 31 December 1945, and in all probability prior to 1 November 1945, Japan would have surrendered even if the atomic bombs had not been dropped, even if Russia had not entered the war, and even if no invasion had been planned or contemplated.

One shouldn't take that as gospel; we actually know more now (from an archival perspective) than the USSBS did then, and they had their own political battles they were waging within the US government (trying to argue for the need of a continued large conventional force in the fact of the apparent "atomic revolution"), but it is still an interesting thing to point out, that this was what even they concluded.

On Japanese anticipation of a Soviet invasion, see Yukiko Koshiro, Imperial Eclipse: Japan’s Strategic Thinking about Continental Asia before August 1945 (Cornell University Press, 2013). On the impact of the invasion of the USSR on Japan's willingness to fight the war, and contrasting it with the atomic bombings, and the pre-bombing "peace feelers" the Japanese put out, see Tsuyoshi Hasegawa, Racing the enemy: Stalin, Truman, and the surrender of Japan (Harvard University Press, 2005).