It's noted that it's not clear how much the atomic bombings influenced the decision to surrender, versus the near-simultaneous declaration of war by the USSR on Japan. Furthermore, by the time Japan surrendered, it was clear that Japan had already thoroughly lost. Recall that similar bombing campaigns against the UK (Battle of Britain) and Germany utter failed to bring those nations any closer to surrender.
In any case, compared to the actual theorists like Giulio Douhet who were, before World War II, arguing that attacking cities would cause the will of the nations to collapse before they fully mobilized, the actual results fell far short of the theorists.
My understanding is that communications between Hirohito and Stalin indicate that Japan was attempting to begin negotiation of a total surrender after Midway and that Truman's diary eludes to this moment. The main argument I've seen to contradict this is that they don't believe Japan wasn't actually going to accept a full surrender at this point.
The US may just as well have dropped 10 more nukes and it wouldn't have changed anything. The Japanese didn't care whether it took a 1.000 bombs to destroy a city or a single one. Even more so, since they didn't know anything about the radioactive fallout and long-term effects. To them, it was just a bigger bomb.