This is without the moral implications. From what I can take of it it seems like the decision would be met with massive political backlash if it hadn't been utilized by the winner of the war. Was fear of the backlash taken into account when making the final decision to drop the bomb? Were the bombs even worth it in terms of the resources used on them?
This is a rather vague question, but I might point you towards two things:
One is the Franck Report, which scientists working on the bomb at the University of Chicago produced in June 1945. It argued that the unannounced use of an atomic bomb on cities would do great damage to American reputation in the Cold War. It did lead to a discussion by the Secretary of War and many top scientists. They decided to drop the bomb on a city, without warning, nonetheless. But it was on some minds.
The other is the discussion over the targeting of Kyoto, led by Secretary of War Stimson. Stimson argued with General Groves over whether Kyoto was a legitimate military target, and convinced Truman that it was not, in part based on postwar considerations.
Other than the above there was not much discussion of backlash. As for whether the bombs were "worth it," it depends on whether you think they ended the war or not (historians debate this), and whether you think either way they were worth building. It is a hard question to answer, because it is based on questions of the value of the bomb, which is a nebulous concept.