I would guess the 4th amendment, but that was removed from the constitution long ago as part of the "war on drugs", where charter operations had their jets seized for transporting druggies (no reference, I saw it on 60 minutes (IIRC) a LONG time ago).
You nailed it. A large portion of the actual and perceived erosion of the 4th Amendment is due exclusively to the WoD. And you first started seeing it via transportation, actually - drug couriers in airports, and on Greyhounds. Reading some of the appellate opinions from the '70's and '80's left my jaw open about what did or did not require "probable cause."
Is a strip search (virtual or real) reasonable simply on the choice of transportation?
The ends don't justify the means (at least, they shouldn't). The 4th Amendment does not authorize a "no holds barred" approach.
Instead, what we've got is a situation where a
situation determines the means that are "reasonably available" to combat it, but those means nevertheless have to justify the ends eventually reached (primarily, conviction and incarceration).
Also, keep in mind that the "reasonable" requirement of the 4th Amendment only deals with whether probably cause is required. If a particular government intrusion is unreasonable, that doesn't mean that it's verboten - it just means that it has to be supported by probable cause (you get an "in-between" with reasonable suspicion for investigatory stops). But, if the intrusion is reasonable, then it doesn't require probable cause or a warrant.
With these things in mind, I don't think there are too many people out there who would say that some degree of intrusion at an airport - when airplanes have demonstrably been repeated targets throughout the last airport - is reasonable. The question thus becomes the degree of intrusion that is reasonable.
Reasonability is a subjective standard. Opinions obviously vary. But, consider this: are the objections to strip (actual and virtual) searches widespread, or are they just vocal? From my observations, it's been more the latter than the former. When you've got a majority of people either supporting, or acquiescing, to a particular something, doesn't that automatically mean that the something is reasonable?
It's easy to say "bah, the majority doesn't know what's good for it." That may be, but then you get into issues of autocracy.
Anyway, if someone were to take this to court, the ultimate answer would be "a virtual strip search, in the face of repeated targeting of airlines using mechanisms that aren't readily detectable by less intrusive means, is reasonable."
Notice that there haven't been a flood of lawsuits filed over the TSA practices. That's because privacy advocates
know that will be the result, and they also can be absolutely certain that once that particular floodgate is opened, there's no telling where it stops.