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.
The Americans did not understand the power of the atomic bomb until it was actually dropped. It was just another weapon of war, a bigger bomb. It wasn't enough to say they had such a bomb without using it. They had to prove that they had it and would use it. No doubt there was an intention to impress the Soviet Union. No doubt the Americans knew it would force Japan to surrender without an invasion or further bombardment with tremendous casualties--but that was doing them a favor by giving them a chance to "save face." The Americans had to drop two atomic bombs to demonstrate to Japan and to the world that they had more than one of these weapons and could build more. Japan may have been willing to surrender before the two bombs were dropped, but they were "negotiating" through other countries. There is probably no proof that they would have submitted to unconditional surrender and occupation and whatever else the Americans wanted to throw at them. There are countless people who would not be alive today if their fathers or grandfathers had had to take part in an invasion of Japan. The atomic bombs were horrible, but the whole war was horrible, and the ending could have been more horrible.