They were already meeting on the night of 9-10 August when news of the Nagasaki bomb arrived, and they were meeting because they had been completely shaken by the Soviet entry into war, which scuppered all their hopes, made the threat of immediate and unanticipated physical invasion on an almost unprotected flank real, and provoked the crisis meeting.
In August 1945 the US was left with only a handful of cities above 100,000 population to bomb. Over sixty cities had already been burned. B-29s dropped thousands of tonnes of bombs on Tokyo and other cities unopposed from spring, 1945. The sea blockade meant Japan was facing starvation. The remaining fleet was sunk in Tokyo Bay. Japan faced starvation.
From the United States Strategic Bombing Survey 1946 report:
'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 [the date of the planned American invasion], 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'
The US Strategic Bombing Survey report is clear that Soviet entry into the war against Japan had been a separate development that Japan had had to consider. Japan had been aware of this possibility from April, when the USSR had stated it would not renew the non-aggression pact with Japan. Though entry of the USSR into the conflict was a possibility, Japan hoped Stalin would remain out of the war and might instead seek to persuade the other Allies to drop their unconditional surrender demand. Their persistent feelers were rebuffed, but Japanese intelligence had missed the massing of Soviet troops and still did not anticipate invasion by the USSR, especially by one of the invasion routes (the Greater Khingan mountains, which were thought to be impassable).
On 11 July 1945 Molotov had refused to sign a peace treaty with Japan, but even still, Japanese hopes were still pinned on the Soviets not invading and focused on invasion from the Pacific. Troops were siphoned from China and Korea and from western Japan to better defend the southern home islands and the east of Honshu and Hokkaido.
The declaration of war by the USSR came late on August 8th and an hour later in early August 9th Soviet troops poured into Manchuria and proved unstoppable. Hokkaido was exposed and so was the rest of northern and western Japan.
The crisis that provoked the SWC meeting was not the overnight destruction of yet another city but the ease with which the Soviets had overrun Manchuria and the fact that they were poised to invade Hokkaido from the west (defence forces were dug in in the east) and dictate their own terms on the Japanese. The Japanese chose to capitulate to the US and negotiate for the preservation of the Emperor rather than taking their chances with a Soviet invasion.