That is the other question that can never be answered, but based on evidence the blood shed would have been much greater if the war had continued on to go on in Japan. It was necessary that the United States dropped the atomic bombs because of a few main reasons. The Japanese leaders were very ruthless and it was against the Japanese culture to give up. For example, Thousands of suicide missions by kamikaze pilots who tried to crash their planes into U. S. warships seemed additional proof of Japanese fantacism.
When Japan refused to give up there was only so much the U. S. could do. When in office Truman argued, That the use of the atomic bomb was necessary to avoid an invasion in Japan that would have cost hundreds of thousands of lives. It is quite possible that Truman may have thought that the atomic bomb could also be used to intimidate other countries like the Soviet Union and the axis powers, but his main focus was the United States at that particular moment in time. There was no winning in Trumans situation because he was basically choosing who lived and who died.
Truman had to choose between possibly losing the war and hundreds of thousands of more men and dropping the atomic bomb on innocent civilians. His actions were not based on the sole purpose of intimidating other countries, but to end the war in the best possible manor without sacrificing more Americans lives. So yes the United States could have quite possible defeated the Japanese, but recent research shows that bombs were the shock that allowed the emperor and peace advocates to overcome military leaders who wanted to fight to the death.
Trumans ecision was an extremely hard one and is something that will continued to be talked about for the rest of time. His actions were for the better good of the American people. Truman had a way for the U. S. to end the war and it is something that was most certainly a burden that lay on his shoulders until he died. Either way you look at it atomic weapons had already been created and because we used them one time they have yet to cause anymore destruction in this world because of their massive power. Truman made his decision for the better good and kept America safe from what could have been a much longer and bloodier war if it had continued.