1. What would have happened? Tremendous carnage of a scale never before seen in that century and the near extinction of Japan as a nation and civilization. Specifically:
--The War Ministry in Tokyo issued an edict that ALL POW's were to be killed before the surrender. Nearly 45% did die in camps (more if you include Asians). But a war that would have lasted 3-6 months longer would have probably resulted in the deaths of ALL Allied POWs. It nearly resulted in deaths of all Chinese POWs (only 56 were alive at war's end) and several camps, all US POWs were killed (burned alive by their captors) while others were put on starvation diets, eaten or beheaded and death rates accelerated. There were even cases of Allied POWs who were beheaded AFTER the Japanese surrender. I can assure you that this would have produced even less tolerance for the Japanese if we'd been involved in an invasion with them as our troops would have come across camps of dead POWs. A friend of mine has an uncle who liberated a POW camp in the Phillipines and that uncle will not buy or use anything that comes from Japan to this day.
--There were have been tremendous US casualties. We estimated 250,000 dead just for the invasion of Kyushu (the southern most island in Japan) and 1,000,000 total. To put that in perspective, our deaths in WW-2 absent this were 418,000 so you're talking about an impact on our nation more than double the existing casualty level. I think the US showed remarkable tolerance for Japan post-war (allowing the Emperor to remain in power, relatively few retributions for war crimes, little financial demands of payment for costs of the war). If we'd had to send in infantry and root out fighters from house to house with the resulting bloodshed and terror, I think we'd have treated Japan differently post-war.
--Japanese casualties would have been through the roof. If we suffered 1 million dead, you can expect their military to suffer worse numbers(which was increasingly turning to suicide attacks, training women to charge our soldiers with bamboo spears, children under 10 to attack tanks with mines which they would blow themselves up with in hopes of taking off a tank tread). You could estimate somewhere between 1.8-3 million dead Japanese "military".
--Japanese civilian deaths would have been horrendous. Here's a stat for you to consider: the first island we captured that had a significant civilian population and was considered Japanese soil was Okinawa (civilians had been evacuated from Iwo Jima). 1/4th of the civilian population on Okinawa believed the lies of the military and killed themselves rather than allow capture by our troops, fearing torture and rape. If even half of that number (ie: only 1/8th) of the Japanese population committed suicide in our invasion than that would have resulted in about 7.5 million civilian deaths. Oh, and you'd better believe that given our experience at Iwo Jima and Okinawa (where Japanese troops burrowed in and forced us to root them out with terrific losses) that our battleships, artillery and ground support aircraft would have heavily prepped all areas before our troops went in. What kind of pounding do you think Tokyo or Kobe would have taken in initial barrages prior to an assault (with resulting civilian casualties)? To project total Japanese deaths (military deaths, civilian suicides, civilian starvation, and "collateral damage") of 12-15 million people is not an unreasonable figure.
--Japan as a Nation would have been a shell of its former self. Ground warfare throughout the entire country would have leveled the cities so they'd all have looked like Hiroshima and Nagasaki absent the radiation. Russia still claims Sakhalin Island as "spoils" from WW-2. With no atomic bomb to prompt a surrender in August, instead a ground war that goes into the Fall, more of Japan would have been captured by the Russians and does anyone doubt that they would have kept it because of the Cold War? Probably all of Korea would have been occupied by Russia as well.
2. But wait, Japan wanted to surrender some people say? Not quite.
--The Allies (including RUSSIA) met at Potsdam in July. Stalin never conveyed any messages from the Japanese. The Allies reached decisions with Japan agreeing that we would FIRST ask the Japanese to surrender and that if the Japanese wouldn't surrender we would use our secret weapon and then Russia would invade. So after Potsdam, per the agreement, the US asked Japan to surrender. If they wanted to surrender so much, why didn't they then? This was prior to the use of ANY of the atomic bombs, prior to Russia's invasion.
--The idea that they were seriously negotiating with the Russians is, well, naive and silly. For starters, they weren't at war with the Russians until August. They couldn't possibly surrender to the Russians. It would have been like Germany suddenly declaring that WW-2 was over, can't invade Berlin because they'd just surrendered to the Swiss! Additionally, the Japanese had a FINE record of negotiation in WW-2. They were negotiating with the US when they bombed Pearl Harbor. Seriously--we were in active, on-going negotiations with them and they attacked us. Why would the Russians take their initiatives seriously--they suffered a surprise attack from the Japanese in the Sino-Soviet war and didn't trust them either. Just how much credibility does anyone really think their negotiations would have had? The idea that all they wanted was their emperor is also naive because they surrendered to us eventually unconditionally (ie: the continuation of the emperor was only AFTER the surrender).
--Remember, we asked them to surrender first before we did anything. They refused. We dropped the first bomb and asked them to surrend. They refused. The Russians declared war on them and invaded and they still refused to surrender. We dropped the second bomb on them and they refused to surrender. The Emperor then personally intervened saying that it was time to surrender. Militarists then held an attempted coup to prevent the surrender. This does not sound like a leadership ready to surrender if only we'd have thrown them a concession or two.
Using the atomic bomb was horrific. But a land invasion of Japan would have completely leveled the country, kill millions of people, resulted in Russian occupation of perhaps as much as half of their territory, earned tremendous hatred and ill-will from the US and resulted in the deaths of nearly a million American soldiers while prolonging the war by about 6 months to a year. Unless the Japanese had surrendered before we conquered all of their territory (in which case not as many people die). But the argument that they were ready to surrender but we wanted to drop the bomb first is just plain wrong. It makes a nice conspiracy theory but the agreements at Potsdam disprove it all.