Obviously the threat of dropping the deadliest weapon ever invented in the history of mankind on one's city is a powerful incentive for peace, but did the US ever consider the possibility that the Japanese government would simply continue fighting? Did the US armed forces have an alternate plan to end the war in the Pacific?
Our very own /u/restricteddata answered a question covering this recently here.
The cliff notes are that the plan, for lack of a better phrase, was to stick to the plan. The bombings of Nagasaki and Hiroshima weren't conducted with the intention of bringing the Japanese to the bargaining table, that is, they weren't a deliberate effort to avoid the planned invasion of Japan, but a way to pave the way for it.
At least, that's what I gathered from his excellent response, hopefully he'll pop into the thread.
The plan was to drop something in the neighborhood of seven more atomic bombs on Japan before the invasion, and then proceed to invade. It was codenamed Operation Downfall, and likely would have resulted in millions Allied casualties. Here is an excellent Wikipedia article on the subject: Link