It wasn't exactly like that, but your characterization is close enough to what transpired. That is, the TSA would have existed but not in the manner it does today if Daschle & Co would have failed to get their way, principally for the purpose of trying to outflank the Ruling Party on so-called security items and appeal to a few core consitutencies and try to build another one up. (The majority party and the Administration could have killed it, but they weren't willing to make a target of themselves or figured it was better to preserve the bipartisan spirit of the time and not make a fight of it.)

In some regards (i.e., certainly not most ), it's more useful to have the TSA "workfare program" displace the private sector, principally as the constitutional rights aspect come into play more strongly. Of course the Administration and the tools in Congress have been more than happy to facilitate "workarounds", even if of questionable legitimacy; and so, public sector or not, the "workfare program" set-up may not provide significantly better protection of civil liberties than if the jobs were done by private sector screeners.