Was the expectation that they'll surrender? If the fear in invading Japan was that they'd fiercely defend it why was the presumption that two bombs would end it? Were they bluffing that was had more bombs and that we'll just bomb everything?
I searched a bit for this and didn't really see it clearly answered or asked.
They had a bomb production system that was expected to produce at least three bombs a month after August 1945, maybe more. They had plans for another bomb to be ready for use around August 17th, a week or so after the Nagasaki attack, but Truman stopped it. It wasn't bluffing that they could have used more weapons if the Japanese didn't surrender, they never made concrete plans as to what to do with more bombs if they had them (see my first link for some discussions of this), there was not a presumption that two bombs would end it (there was a hope, but even General Groves, the head of the bomb project, thought it would take at least two, maybe as much as four). And they would have nuked and invaded if the Japanese hadn't surrendered — that was the explicit plan, and in fact the Americans were caught a bit off guard by the rapid surrender.