I would certainly have supported the use of the atomic bomb if I had been an American living at the time of World War II. There would have been two reasons for this.
First, we have to realize that the average person at the time of WWII would not have had any idea of what the atomic bomb really was. There was no real understanding of radiation sickness. The average American would not have known that the bomb would cause cancer among survivors.
Second, even if I had known those things, I would likely still have approved of using the bomb. I would have approved because I would have wanted the war to be over as quickly as possible with as few American deaths as possible. I would have seen the atomic bomb as a good way to accomplish this. I would have thought of the battles at Saipan and Iwo Jima and Okinawa. They would have made me feel that an invasion of Japan would have cost huge numbers of American lives. I would have just wanted to do anything possible to end the war and to do so without risking any more American lives.