The supposed goal of the TSA is to efficiently and effectively protect travelers and the country from criminal and terrorist actions. In theory, if the TSA is doing its job well, it's actually reducing budgetary needs and slashing fat in favor of efficiency. The TSA should be trying to become clever and nimble, moreso than massive and overhead-burdened.
But the self-preservation mandate suggests the opposite. Self-preservation, for a government agency, means making sure you preserve or grow your budget year over year -- because you're fighting other agencies for it. Every dollar you get is up for grabs by other agencies next fiscal, and vice versa. Accordingly, becoming expensive and inefficient works in favor of self-preservation. As any seasoned bureaucrat knows, not achieving results means asking for more money to throw at the problem. If the TSA demonstrated that it was achieving its goals at current budget levels, it wouldn't receive the same budget next year. Or even face a budgetary reduction.
(1) they serve some reasonably obvious positive purpose
(2) the negative effects of what they do aren't too noxious, in particular when compared with (1)
The TSA, it would seem basically fails on both points. Despite the good intentions with which it was formed, it's pretty clear that they don't improve safety in any significant manner (you might find people some disagree about this, because they believe the security theater, but I think the number is dropping). The negative effects of their existence, of course, are legion, (I suspect it's quite hard to find anybody that disagrees on this point!).
So I'd suggest the public probably on average doesn't support the TSA to the same degree they might other bureaucracies, even those that they find annoying.
Unfortunately, of course, the public's opinion on the matter is of little importance once the system is in place...
But when they prioritize self-preservation over their intended goal, that's bad.