Based on a cursory reading, I don't believe the United States underestimated the death toll. The bomb itself was known to be devastating. Einstein himself petitioned the government to with hold the use of the bomb, knowing full well that the weapon was many orders of magnitude more dangerous than any sort of conventional bombing technique used up to that point.
You can see in both the crewman's account and in the Potsdam declaration, that the United States had foreseen the affect of the bombing, "utter destruction" and "utter devastation", "an act of war to end the war." The Americans knew what they were doing and they knew the death toll with be staggering. They weren't intending to hit a bridge or a road. They were trying to disable the Japanese completely. The stakes were so high that they were willing to sacrifice any number of people to end the war.
In short, no, the Americans didn't overestimate or underestimate they simply gambled that it would do what was needed. And in that at least, they were correct.
Crewman's account of the bombing
I'm going to hedge the above claim by pointing you to this. It's well sourced and seems to be relatively contradictory to my statements.