The Americans had already used the bomb, twice, and even before that there wasn't really any doubt they would if they could. As history proved both before and after Nagasaki, the US was happy to cause any amount of death and destruction to fight the (mostly extremely paranoid and overstated) 'threat of communism'. And whatever you think about the idea of nuclear deterrence in the modern era, there's little to no doubt it was the only thing preventing the US using nukes against the USSR.