Liberals spent the anniversaries of the Hiroshima and Nagasaki nuclear bombs explaining how American intelligence thought the Japanese would have surrendered without them. It's funny how the left thinks intelligence is gospel when it backs their point of view, and garbage when it says Saddam Hussein has weapons of mass destruction.
The casualty estimates for the invasion of Japan included 500,000 to 1,000,000 dead Americans and at least twice that number of Japanese dead. The military believed the casualties for the invasion would be so high that they ordered 500,000 Purple Hearts, the medal awarded for wounds sustained in combat. Because the Japanese surrendered after Hiroshima and Nagasaki, we luckily didn't need them. Today, we still have 120,000 of the Purple Heart medals made for the invasion of Japan in inventory. The number of Japanese killed by the two atomic bombs totaled about 225,000. My father was in the US Army in the Philippine Islands when the war ended. He knew he was going to Japan. Links are to invasion casualty estimates and atom bomb deaths.
My personal opinion is that the Emperor would not have been able to force the Imperial Japanese Army to surrender without the Nagasaki bomb. Accounts I've read, and I've read quite a few, all say that resistance to surrender from Japanese Army commanders was very strong until Nagasaki made their position crystal clear. The Japanese Navy had no doubt it was beaten, but the Japanese Army had not seen defeat that closely. Remember that naval units could flee a lost battle in the Pacific without losing face. Japanese Army units fought until everyone was dead, so the Japanese Army had no first hand reports of their defeats.
You should also note that the reason Admiral Isoroku Yamamoto was in charge of planning Pearl Harbor in 1941 was that the Army had threatened to assassinate him. Yamamoto had been the Japanese Naval Attache in Washington, DC, spoke English well and had traveled extensively in the US. Yamamoto predicted that Japan would lose in a war with the US, so the Japanese Army wanted to kill him for being so defeatist. The Navy ordered him to sea duty to keep Yamamoto alive, which is how he became the Japanese fleet commander. The Japanese Imperial Army really was an organization of war mongers who would kill anyone who got in their way. Many historians have speculated that the Army would have gotten violent with the Emperor, perhaps imprisoning him, if he tried to surrender before the Army wanted to quit fighting.
When considering the death toll from the bombings, remember it wasn’t just American lives at risk in a potential invasion. Almost the entire Japanese population was going to fight. Their defense plan in 1945, named Operation Ketsugo, called for the use of the Civilian Volunteer Corps, a mobilization not of volunteers but of all boys and men 15 to 60 and all girls and women 17 to 40, except for those exempted as unfit. They were trained with hand grenades, swords, sickles, knives, fire hooks, and bamboo spears. These civilians, led by regular forces, were to make extensive use of night infiltration patrols armed with light weapons and demolitions. See the link.
Even in the face of all of the facts, some folks are upset about the civilian death toll at Hiroshima and Nagasaki. The Japanese didn’t recognize much of a distinction between soldiers and civilians. If you want an example of how the Imperial Japanese Army viewed enemy civilians, consider the Rape of Nanking. See the link.
Stubborn liberals say the second bomb dropped on Nagasaki was not necessary. Here’s a link to the play by play of the Japanese cabinet deliberations that shows the second bomb was necessary. The Japanese had doubts about surrendering until after the second bomb.