If I was Commander in Chief, I would of used the bomb without question, every time for many reasons.
1. Would it save American lives? Yes, as President you are responsible for the military and their lives.
2. Would it demonstrate to the Russians to conclude the war, rather than continue it? Yes, Russia would be much less willing to attempt to gobble up Western Europe after the Allies were shipped home.
3. Would it save Japanese lives? Yes, far more Japanese lives would of been lost (civilian and military) if an invasion occurred. If you need proof of that, watch the civilians jumping off the cliffs in Saipan and the military flying one way trips to our fleets in everything from aircraft without landing gear and rockets with a bomb in front of them (Ohka). Heck, they didn't even surrender after the first bomb was dropped, do you think they would have surrendered to an invasion fleet?
Frankly, whoever says they would not drop it is kidding themselves and not putting themselves in Truman's shoes.
edit: I'm not a hawk, I hate nuclear weapons and the very threat they continue to pose today, especially from smaller devices in the hands of rogue states/terrorist groups.