From Mission With LeMay, page 369:
Suppose that you are interviewing me now. Suppose that you ask, “If you had had the incendiary bombs in your stockpile, the ones you asked for and didn’t get, would you have flown more incendiary missions against Japanese targets, just as fast as you could mount them?”
“Yes.”
“Do you think those attacks would have been as effective as the first series which occurred in March?”
“Yes. Probably even more so. The destruction and demoralization in Japan was being rapidly accelerated. Had increased like cube root.”
“Do you think that by relying solely on incendiary attack, you could have knocked Japan out of the war, thus precluding any invasion of the Japanese homeland until after the collapse came?”
“Yes. I think it could have happened.”
“Then it would have been possible to force Japan out of the war, and thus end the conflict, without actually employing atomic weapons?”
“It might have been possible.”
I don’t want to be a Monday morning quarterback. Never did. I’ll say again: I think it might have been possible.
It depends what the goal of defeating Japan was. If it was the reason the US and British gave for cutting off their oil supplies before Pearl Harbor, i.e. end Japanese imperialism in Asia, that was already accomplished by forcing them back to their own island. If the goal was (for the first time in American history) unconditional surrender of an enemy, well unprecedented demands cause unprecedented resistance which could only be overcome with an unprecedented response.
An excellent examination of this topic (available from JSTOR):
Hiroshima and the Historians: History as Relative Truth, KENNETH B. PYLE, The Pacific Northwest Quarterly , Summer 2013, Vol. 104, No. 3 (Summer 2013), pp. 123-132