We're doing a debate in APUS History tomorrow on this topic and I am arguing that the US was justified. My specific role is to ask questions to poke holes in the other sides arguments. So far, my only question is "What alternative could the US have taken to end the war unconditionally, and how would the alternative compare in terms of both American and Japanese deaths?"
See the FAQ section on Japan and the atomic bombs
A major argument is that it was seen as the better route to take than a land invasion of Japan, which would have inflicted major casualties ob both sides. American estimates range from 280,000-1,000,000 on the Allied side alone.
http://www.pbs.org/wgbh/americanexperience/features/general-article/pacific-operation-downfall/
http://www.airforcemag.com/MagazineArchive/Pages/2009/June%202009/0609invasion.aspx
Depends on how you want to frame it.
Everyone was tired of the war, the US absolutely wanted unconditional surrender and at that point in the war the Japanese were still a bit lukewarm on the idea. They were trying to cut a deal where the Soviets would intercede on their behalf, but the US really wanted to drive home the idea that the Japanese government really needed to stop trying to avoid the elephant in the room- the US was bombing everything it could, and the driving narrative behind the nuclear bomb wasn't so much, "we can kill this many people and do this much damage" as "We can do this with one bomber now. Its time to throw in the towel." Because the casualty figures for the nuclear bombs were unremarkable against other major bombing operations- fire bombing Tokyo claimed comparable figures.
Furthermore, realized operations to invade Japan figured that anywhere from hundreds of thousands to a million troops would be lost in the endeavor.
A lot of revisionists like to put some clever (potentially dumb) spin on the fact that the Japanese high command didn't really have an immediate reaction to the bombings, and the fact that after bombing out 40 or 50-some-odd major cities and other noteworthy targets meant that the last two were insignificant, but that's just being unreasonable.
Depending on how you look at it, the nuclear bombs were both unremarkable, and game changing, and the Japanese had every reason to assume that the US had more in reserves, even though it'd really take months for the next bomb to be completed.
So....
1: The Japanese were ready to surrender but
2: The terms weren't what the US wanted, and they didn't like the idea of having the Japanese convince the Soviets to intercede on their behalf.
3: While the destructive capabilities of the operation weren't remarkable against other such endeavors
4: what it did with just a single aircraft was.
"Justified" is a matter of perception. The war crimes of Japan were apparent at this point. Everyone was tired. You might look at it as justification, or you may just think Trueman had a really big hammer, and the only nail left was Japan.