The estimates of American casualties for an invasion of mainland Japan was in excess of 1 million Americans. Possibly in excess of 2 million Americans. The United States dropped two atomic bombs to save American lives and speed the end of the war.Prior to using the atomic bomb, Japan was given ultimatums to surrender along with warnings of the dire consequences. The Japanese government ignored the warnings.he estimates of American casualties for an invasion of mainland Japan was in excess of 1 million Americans. Possibly in excess of 2 million Americans. The United States dropped two atomic bombs to save American lives and speed the end of the war.