By your own numbers - 60k employees just doesn't touch a jobs program in a country of 350M people. The point of a jobs program is to provide jobs.
TSA was created to accomplish a goal - security theater (mostly), preventing another 9/11 (maybe more in theory than in practice), etc.
The New Deal WPA, according to wikipedia, supplied about 3M jobs at its peak in 1938, when the population was ~130M.
2.3% of the population vs 0.017%.
Also empirically - if it was a jobs program, it would be way better staffed..