As with any large and complex organization, staffed by real human beings, motivations could vary. For some it was clearly about a fear that if the US did not build the atomic bomb first, the Nazis would probably do so. It is clear that for some of the scientists, notably some at the very top of the hierarchy, this was indeed a real fear until late 1944. This sort of fear (do before literally the worst people in the world do it) can be a strong motivator.

As for other motivations, one could speculate based on memoirs, human psychology, what have you. Being "in on the action" for a new endeavor, especially one of a massive scale (scientifically, industrially, politically), one staffed with Nobel Prize winners — all of this is good for one professionally, and it would be foolish to discount that social aspect of it.

It should be kept in mind that the number of scientists was about 1% of the whole labor force of the project. That is, most of the people working on the project — some 500,000 of them — were not scientists or engineers, but laborers or operators whose educations and knowledge of what they were working on was much more limited than the scientists. Even the scientists were, depending on which site they worked on, were compartmentalized ("need to know") to various degrees. If you didn't know it was an atomic bomb project, you were told that it was simply important war work, which, during a major war, was enough to keep a lot of people on the job. On the other hand, they also had a phenomenal turnover rate — the work sites were pretty awful, and so at some of them they lost upwards of 20% of their staff every month as a result, requiring massive recruitment and retention efforts.