supporters of using the atomic bomb against japan at the end of world war ii thought an invasion would\ncost…

Brief Explanations:

Supporters of using the atomic bomb against Japan at the end of World War II were concerned about the potential loss of American lives in an invasion. Historical context shows that estimates of casualties in an invasion were high, and using the bomb was seen as a way to avoid that. The other options are not as strongly supported by historical reasoning. An invasion of Japan was planned and was expected to be a large - scale operation, but the main concern of the bomb's supporters was the human cost. There is no strong evidence that an invasion was thought to be unsuccessful (the US had significant military strength), opposition by the American people was not the main factor (public opinion was more about ending the war), and the ship - building aspect was a logistical detail compared to the life - and - death issue of casualties.

Answer:

cost too many American lives.