There are different versions of the story. In one of them, somebody asked the question whether the atmosphere could ignite, and that was very quickly answered in the negative, but then Oppenheimer mentioned it to the people in Washington, and after that the question recurred periodically because the higher ups got unduly alarmed.

And then of course there are versions making it into a much more dramatic story.

When they were working on the fusion bomb (and Edward Teller was working on fusion full time already during the Manhattan project), it took some years to establish that even the "easy" to fuse deuterium cannot be set of by simply blowing up a fission bomb. The reaction simply did not propagate for any reasonable dimensions of the system. For any other material the energy balance would have been orders of magnitude short of what was required for a propagating fusion burn.