How long would WWII have continued had the US not used the atomic bombs?

While invading Japan itself would have been a very tiresome and bloody enterprise the atomic bomb wasn't even needed to convince Japan to surrender.

The biggest problem towards the end of the war was the way it would surrender, the Americans demanded an uncontional surrender, as Germany had done. Japan however was willing to surrender but wanted at least so safeguard the Emperor. On the other hand they seemed to be willing to fight as long as the only possiblity to end the conflict was an uncontional surrender.

The irony is that even after the two atomic bombs and the surrender of Japan they managed to retain the institution of the Emperor.