I used to believe that invading Japan would take a million lives. Those high estimates of casualties have been dropped dramatically. What has come out is that the Japanese were trying to surrender, with the main impediment being the fate of the Emperor. I doubt an actual invasion would have been necessary because the Japanese were on the verge of starvation. Six months is the figure given by scholars before capitulation by Japan. From the link:
"It didn't take long after the atomic bombings for questions to arise as to their necessity for ending the war and Japan's threat to peace. One of the earliest dissents came from a
panel that had been requested by President Truman to study the Pacific war. Their report, The United States Strategic Bombing Survey, was issued in July 1946. It declared, "Based on a detailed investigation of all the facts and supported by the testimony of the surviving Japanese leaders involved,
it is the Survey's opinion that certainly prior to 31 December 1945 and in all probability prior to 1 November 1945, Japan would have surrendered even if the atomic bombs had not been dropped, even if Russia had not entered the war, and even if no invasion had been planned or contemplated." (Bernstein, ed., The Atomic Bomb, pg. 52-56)."
Hiroshima: the Article