Supposing that the Manhattan project doesn't produce a bomb before ~1947 for whatever reason, Japan would neither have surrendered nor died before 1947. The Soviets were in no position to invade the home islands in 1945, nor would they be in such a position in the forseeable future. At that time, the United States was faced with two options--maintain a blockade for a possibly indefinite period of time against the Japanese, perhaps until they were expected to surrender in 1947, or invade with all due haste. It was a fork in the road, one-or-the-other.
Were the United States to engage in a blockade with the possibility of an invasion if Japan did not surrender, America would have to maintain a standing army and near full mobilization for two years without action. By this time remember, people are already getting weary of the war. Maintaining a 7-million man army in what's effectively peacetime will be very unpopular: a quick solution is needed. If the bomb wasn't available and an invasion wasn't launched by late 1945, it's likely Japan would have been able to negotiate a (harsh) peace.