The 'clear argument' is no such thing. Japan did not accept the Potsdam Declaration until August 10, after both the atomic bombings. Even then, the Japanese could not bring themselves to negotiate directly with the United States, attempting to mediate through the Soviets until their invasion of Manchukuo on August 9.
While it is quite true to state that Truman's decision to drop the bomb was influenced in part to avoid the Soviet Union's entry into the Pacific War 90 days after the defeat of Germany as promised by Stalin, to avoid a potential change to the political landscape of East Asia. it also true that the Japanese War Cabinet did not accept the Potsdam Declaration until expressly ordered to do so by Hirohito. Even then, the Kyūjō Incident, an attempted coup, reflected the willingness of certain radicals to continue fighting even after the atomic bombings of two cities and the Soviet invasion of Japanese-controlled territory.
That said, both Hiroshima and Nagasaki were targets of military significance even in the destruction of 1945 Japan, and Hirohito himself noted the power of atomic weaponry in his 'endure the unendurable' surrender message. Clearly the American nuclear decision played a significant role in Hirohito's decision.
To other facts: Operation Downfall, which consisted of the planned invasion first of southern Japan (Operation Olympic, 1945) and the invasion of the Kantō plain near Tokyo (Operation Coronet, 1946) had a casualty estimate of at least one million, with the numbers rising depending on the extent to which Japanese civilians resisted the invasion. It is also important to note that the Japanese Army was still quite formidable even as late as the summer of 1945, holding huge swaths of occupied China and Manchuria.
The idea that somehow the Japanese would have simply stopped fighting despite increasingly fanatical resistance to Allied power projected across the Pacific is not borne out by any serious scholarly work of which I'm aware.
It is more than defensible to hold the position that without Hirohito's order to accept the Potsdam Declaration, the Japanese would have continued to fight.
The best work on video that I've seen about this issue is Part 25 of "The World at War", entitled simply "The Bomb". Excellent documentary television which features interviews with some of the key contemporaries of the day.
It’s also defensible to say, as Eisenhower did, that their defeat was inevitable. the blockade of Japan was already having a mammoth toll.