The entire point of the bomb was to be a surprise, shock attack. Hence all the secrecy about it towards the end of the war. They were not afraid of it being a failure (they had already tested it by that point). Operationally they had concerns about the Japanese knowing it might be used because they could try to intercept it, but that would have been hard anyway and in any case played no apparent role in the Potsdam question.

On Potsdam in general, it is clear if you go over the discussions/diary entries/etc. that nobody thought Potsdam would cause the Japanese to surrender and that Truman and Byrnes in particular were not willing to make modifications that might increase that possibility. The goal was to put out a statement that says, "surrender, or else!" and then drop the atomic bomb. The statement and its rejection would give a sort of moral/ethical fig-leaf to the lack of warning, and not diminish from the "shock" of the atomic bomb (and the invasion of the Soviet Union, which the Americans hoped the bomb could avoid, but still knew would have a profound affect of the Japanese if it happened).

I think the fundamental issue here is that a lot of people wonder, why didn't the US warn the Japanese?, which in some ways misunderstands the US view of the atomic bomb altogether. There were many reasons that many people involved in the creation of the bomb wanted to actually use the bomb on a city — they thought it would have a profound effect not just on the present war, but on future possibilities of war as well. To end the war without using the bomb would have been perceived as a failure on behalf of the people who worked to make the bomb.