So this is a tricky issue. One can find a variety of claims about potential claims to casualties (which, we should note, are not the same thing as deaths) prior to Hiroshima. There are both "high" and "low" estimates that were made by various parties in the US government and military. There are a sum total of four estimates that were made that had extremely high numbers (e.g., close to a million casualties); none were made by high-level advisers, and there is no evidence that these estimates made it to the high-level advisers who had input into the war planning or that these estimates played any role in them.

The one meeting we have evidence of for high-level planners, including Truman, where projected casualties were discussed, the consensus among the admirals and generals was that they would be in the low hundreds of thousands or even the tens of thousands. Generally speaking they were optimistic that it would not have the high casualty or fatality ratios of the island-hopping campaign because the physical size of the Japanese home islands meant that they would have many more options with which to approach them strategically, as opposed to the very unfavorable conditions at places like Iwo Jima or Okinawa. It may be that they low-balled the estimates, because they wanted Truman to approve the invasion (he approved the invasion of Kyushu, by not Honshu, in the summer of 1945). But either way, those are likely the only numbers that Truman had on his mind. Big numbers, to be sure, but not as big as the more inflated numbers that would be used later.

So what's up with the Stimson article? Stimson wrote the Harper's article in late 1946 as an attempt to shape the emerging narrative on the atomic bombs. There had been criticisms of their usage from high-level military figures (including Admiral Leahy and General Eisenhower) after the war ended (they argued they were unnecessary) and there had been growing concerns from other quarters as well (e.g., John Hersey's Hiroshima put a lot of focus on the civilian experiences). Stimson wrote the article, at the urging of people like James Conant and Leslie Groves (two principle participants in the Manhattan Project) to "set the record straight" on the bombings. But he wrote it in a way that in retrospect is not very historical (and arguably not entirely honest, though it is possible that Stimson doctored his own memory as well). It creates many of the important "official narratives" of the use of the bomb — such as the idea that there was a reasoned "decision to use the bomb" by the President that balanced the loss of life from an invasion versus the atomic bombings. Hence the need to invoke a very large loss of life indeed; if you start saying that it is worth massacring hundreds of thousands of civilians (who did not enroll in the war) to save the lives of tens of thousands of soldiers (who did), you start to very quickly get into tricky moral and ethical territory. If your number of lives saved goes way, way up — well, then it seems self-evidently the better option.

Either way, it utterly misrepresents both what the decision-making process was (there was no singular "decision to use the bomb," it was never framed as "bomb or invade," Truman's role was mostly nominal), and what was known at the time (they didn't have high casualties on their minds, they weren't sure it would end the war, etc.).

Today people use high estimates of invasion deaths for the same purpose, usually without contextualizing them. Be wary of any and all such claims — or, at least, contextualize them (who claimed them, and why).

For a detailed discussion of all of the various claims and who may or may not have seen them, see Barton J. Bernstein, "Reconsidering Truman's claim of ‘half a million American lives’ saved by the atomic bomb: The construction and deconstruction of a myth," Journal of Strategic Studies 22, no. 1 (1999). For a very excellent history of Stimson's article, see Gar Alperovitz, The Decision to Use the Atomic Bomb and the Architecture of an American Myth (Knopf, 1995), part IV, "Managing History." (There is much I disagree with in Alperovitz's book, but he does the best job of discussing the postwar efforts to shape the narrative that I have seen.)