The key part of a negotiated verses unconditional is that we could not approach Japan, they had to be willing to accept our terms. If we initiated then Japan would have every incentive to keep fighting to get better terms. Could Truman really go to the American public and say we are agreeing to let Japan dictate terms to us? The reason both the bomb and the Soviet invasion were both key is the bomb demonstrated that we would in fact destroy Japanese cities with out invasion and the Soviet invasion took away Japans hold on the territories it thought it could hold on to.
Has this been posted? It's worth a read: Casualty Projections for the U.S. Invasions of Japan, 1945-1946: Planning and Policy Implications by D. M. Giangreco Whatever the casualty projections may have been, and however we might look at them with hindsight, in 1945 they were seen as entirely credible.
Something went wrong with my post - the info above comes from tapes collected for the World at War Series but not used. Toskikazu Kase was Secretary to the japanese foreign minister (he was actually a member of teh delegation on the Missouri) It does seem to shed some light on the involvement (or rather non-involvement) of the USSR in the peace negotiation process.