The might that now converges on Japan is immeasurably greater than that which, when applied to the resisting Nazis, necessarily laid waste to the lands, the industry and the method of life of the whole German people. The full application of our military power, backed by our resolve, will mean the inevitable and complete destruction of the Japanese armed forces and just as inevitably the utter devastation of the Japanese homeland.
Those are pretty unequivocal terms, if you don't surrender we will destroy your army and your land. And it is not like the Japanese didn't know this was the inevitable conclusion of the conflict. Germany and Italy had already surrendered and Japan was left alone, battling the might of the US, UK, China and the Soviet Union, which just entered the conflict. They must have had some sense of honor which told them that, despite it being a lost cause, they would be willing to fight house to house against a superior foe, sacrificing millions for nothing. It's pretty clear that the casualties, to both Americans and Japanese, would have dwarfed the casualties in Hiroshima and Nagasaki had we not dropped the bomb and scared the living daylights out of the leadership. Think about it, between 150,000 and 250,000 people were killed in the bombings of the two cities, however you had 95,000 Japanese soldiers killed in just the battle over the small island of Okinawa and 205,000 Japanese soldiers killed in the battle of Luzon. You also had about 500,000 people killed in a conventional strategic bombing campaign which laid waste to 67 Japanese cities and destroyed over half of Tokyo (one city, Tokoyama saw 99% of its area destroyed).
It is pretty clear that we have zero reason to apologize, and if anything the atomic bombs saved lives. So why did the President of the United States want to apologize? It just boggles the mind. I have to wonder, who else did he apologize to or try to apologize to? I wonder if he apologized to the Iranians for our support of the Shah. At this point it wouldn't surprise me.