There was entirely a different mindset by Americans in that war than there has been since. Every family was involved in some way with the war, either having a relative in the service or in some way working or volunteering in the war effort. Food (especially meat and sugar), gasoline, tires were strictly rationed.
The news media covered the incredible brutality of the Japanese who had attacked us at Pearl Harbor without warning. The Bataan death march, a photo in Life Magazine of an Australian prisoner about to be beheaded and press reports and newsreels of the enormous casualties at Iwo Jima and Okinawa, did not leave Americans with a warm and fuzzy feeling about the Japanese.
Wars are won by swift, decisive action. The comparison of WWI with its drawn out trench warfare and the German blitzkrieg in 1940 is an example. Despite millions of deaths in WWI, Germans never got within 70 miles of Paris. In 1940 with surprise and overwhelming force, France fell in 38 days with minimal casualties on both sides.
President Truman in 1945 was faced with the same realities. He could use a dramatic new weapon that could end the war quickly, or he could order the invasion of Japan. With the experience of Iwo Jima (6,822 KIA, 19,217 WIA in 33 days) and Okinawa (12,513 KIA, 38,916 WIA in 82 days), projections of US casualties varied from about 100,000 to 250,000 killed depending on the duration of the campaign.
So he did what was necessary, and the Japanese announced their surrender 9 days after the first bomb was dropped on Hiroshima. What would have happened had we not used the bomb? Would there have been a political reaction from the hundreds thousands of families whose children or brothers had been killed or wounded? You betcha!
The secret of the bomb would not have remained secret. And the wanton waste of life would have become a major political issue. At best Truman would not have survived the election in 1948. But there is a distinct possibility he would have faced far worse, impeachment.