I recently read in Marching Orders, by Bruce Lee, that Eisenhower was against using the bomb on Japan for moral reasons, as were a great many others.. MacArthur was against using it because he wanted to lead the largest invasion in world history. In Hasting's book, Armageddon, he tells how, while all the other casualty estimates ran in the hundreds of 1000's, even millions, MacArthur insisted that there would be no more than 31,000 American casualties. He really did not care how many bodies he had to stand on to achieve that pinnacle.
Richard B. Frank, Downfall: The End of the Imperial Japanese Empire, has this to say about MacArthur's casualty estimates. One, MacArthur gave two figures, the first was in the millions, the second figure was more precise because Truman demanded specifics. MacArthur's numbers were the following for Olympic and Coronet:
D-Day - D+30 = 50,800 battle casualties
D+31 - D+60 = An additional 27,150 battle casualties
D+61 - D+90 = An additional 27,100 battle casualties
* Note, MacArthur's staff deducted casualties who could return to duty, which are the majority. And did not count those lost to sickness or injured in accidents, which accounted for roughly 1/4-3/4 of total losses.
Overall, casualty estimation is like water dowsing, its bull. The boss (Truman) wants an estimate to make a political decision but its completely impossible to give a detailed response. There are simply too many factors to consider, and most of them are unknown. Realistically, considering the level of resistance, the manner in which the Japanese had correctly guessed the invasion beaches, their use of kamikaze (air, ground, naval), if the US had attempted any conventional invasion it would have been worse than any of the casualty estimates given by Nimitz, MacArthur, or those of the Joint Chiefs.
Lastly, those who were read in on the atomic bombs at the level of the Joint Chiefs were thinking of using between 10-12 atomic bombs tactically just to support the Kyushu invasion. Which further illustrates how impossible it would have been to estimate US casualties.