We don't really know. The plans prior to Hiroshima and Nagasaki were to drop atomic bombs and invade. The strike order made it clear that this was a very open-ended mandate; the military could drop bombs as soon as they were made available.

However after Nagasaki, Truman put a kibosh on that and said that no bombs could be dropped without his explicit permission. So it became a much more "political" process, as opposed to a simple "use as available" process.

In the wake of Nagasaki, and before Japanese surrender, there were discussions among the military about what to do next, and there were some (including General Marshall) who seemed to be leaning towards saving up a bunch of bombs and then using them to support an invasion (which is to say, tactically), as opposed to city bombing (which was feared to have lost its psychological effect). But there were others who just thought they ought to drop one on Tokyo.

Just before the actual surrender, there was a growing sentiment in Washington that another bomb ought to be used, and the Manhattan Project personnel were getting ready for an order to ship their third core to Tinian, and Truman told the British ambassador that he "sadly" might have to order another bomb used on Tokyo. But the surrender came only a few hours after this.

Which is to say: there was a sentiment before Hiroshima/Nagasaki, but it isn't clear it mattered after it, as things changed very rapidly. The surrender came fast-enough that no real future plan was made. I think it's possible they might have used a third bomb fairly soon after that if the war had gone on. But in terms of a longer policy, it's impossible to say; they were plainly playing it by ear.

For a long discussion of this, see Gordin's Five Days in August. For a very focused discussion of this question, see an article I wrote last summer for National Geographic History: "Did the U.S. plan to drop more than two atomic bombs on Japan?" (mirror)