At the time that the decision to drop the bomb was actually made, there was very little discussion of the issue. Winston Churchill, for example, said later that it was just assumed that the bomb would be used if it became available. There was no extensive discussion on any formal level.
There are plenty of people who stated after the fact that they had believed that the use of the bomb was not necessary. However, in most cases, it is not at all clear that they actually believed that in the days before the bomb was dropped. If they did in fact believe it, they did not make any strong arguments against using the bomb.
The major argument that people made in 1945 and the following years was that Japan was ready to surrender. They argue that the war was going so badly for the Japanese that they would inevitably have given up without the use of the bomb or an invasion.
In later years, other arguments have sprung up. More people have argued that it was immoral to use the bomb because it was in some way worse than destroying cities with conventional bombs. They have argued that the US used it for racist reasons. They have argued that the US used it only to scare the Soviet Union. These arguments, however, were not made at the time.
Thus, if anyone really disagreed with using the bomb in 1945, it was because they thought the Japanese would surrender even if the US did not use the bomb.