In 1945, there was really very little in the way of different views about this decision. Dwight Eisenhower did argue against the use of the bomb. However, he was the commander of forces in Europe, not in the Pacific. Winston Churchill indicates that there was little debate. The bomb was seen as something that could end the war quickly and with no casualties on the American side. After almost four years of total war, this was something that American leaders welcomed.
Since then, there has been a great deal of controversy over the decision. Many people argue that the US did not need to drop the bombs. They argue that Japan was on the verge of surrender even without the bombs. They claim that the US used the bomb, at least in part, to scare the Soviet Union and to put the US in a stronger position for the Cold War that seemed likely to arise after WWII ended.
The different views today, then, differ as to whether the bomb was really necessary and whether it was dropped for motives other than ending WWII as quickly as possible.