From a legal perspective there's actually a valid point here: they're not conducting universal searches for evidence to use in criminal prosecution, which is mostly the sense that the 4th Amendment is interpreted as applying to. Rather, they're simply enforcing a mandate not to let certain types of objects enter a specified area. Effectively they're arguing that it's no different from, say, a courthouse which has a "No Firearms Permitted" sign on the door and guards and metal detectors to enforce that policy, and for the most part such things are widely accepted to be constitutional.
The main way to fight these "administrative searches" is to show that they are too invasive, or not narrowly tailored to achieve their purpose, both of which are criteria US courts have shown they care about.
> In April 2012, during a joint operation with the Houston police and the local transit police, people boarding and leaving city buses complained that T.S.A. officers were stopping them and searching their bags. (Local law enforcement denied that the bags were searched.)
> The operation resulted in several arrests by the local transit police, mostly for passengers with warrants for prostitution and minor drug possession.
Not really meeting the criteria you're talking about.
Meanwhile, universal searching (at first by metal detector, later by other means) of passengers at airports has long been held constitutional by courts; if they step outside the boundaries of what's permitted, you can haul them into court over it.
The main way to fight these "administrative searches" is to show that they are too invasive, or not narrowly tailored to achieve their purpose, both of which are criteria US courts have shown they care about.