You specifically asked how many would die, but almost all the estimates I've seen are for the number of casualties. I suspect that in popular discussion the two get confused a lot. With your indulgence I'll address the number of casualties.

The projections varied wildly, based on who was making the estimate, when you're talking about (estimates were constantly changed as new intelligence became available) and on what the goal was. That last one may sound odd, but there was much debate about whether holding a few key areas (Tokyo, etc.) would be sufficient, or on the other extreme, the mountains would have to be flushed out. Of course politics also played a role.

The lowest estimates I've seen were from MacArthur, with 105,000 casulaties. The JCS estimates at one time "implied" 2M, but were revised down to 500k. Much of army planning for obtaining additional troops, medical and transport requirements were based on a figure of 720k. So pick a number anywhere in that range and you can make an argument that that was "the number".

One of the key reasons the estimates varied so much is that it depended on what former battle's casualty rates were considered as the more realistic scenario for Japan. Normandy, Saipan, Iwo Jima, Okinawa, take your choice. There were also factors such as an assumed learning curve, meaning that as the invasion went on the US troops would learn how to more effectively combat Japanese tactics. Also as I mentioned previously estimates were revised constantly based on incoming intelligence. For example in the earlier planning it was estimated that the Japanese had three divisions in the southern part of Kyushu, which is where the first stage of the invasion was to take place. Later it was learned that the Japanese were moving another seven divisions there. Estimates of things like Japanese fuel reserves and how many planes, tanks, etc. they had stashed away also varied over time.

There is a good paper about this from the Journal of Military History, Casualty Projections for the U.S. Invasions of Japan, 1945-1946: Planning and Policy Implications.