It turns out that the most relevant case is one from the U.S. Court of Appeals for the Ninth Circuit (United States of America v. Daniel Kuualoha Aukai) which ruled that:
We have held that airport screening searches, like the one at issue here, are constitutionally reasonable administrative searches because they are “conducted as part of a general regulatory scheme in furtherance of an administrative purpose, namely, to prevent the carrying of weapons or explosives aboard aircraft, and thereby to prevent hijackings.”And because "the Supreme Court has repeatedly upheld the constitutionality of so-called “administrative searches,.” it is reasonable to assume that the Supreme Court would find these searches constitutional, generally.
The caveat to this decision:
Although the constitutionality of airport screening searches is not dependent on consent, the scope of such searches is not limitless. A particular airport security screening search is constitutionally reasonable provided that it “is no more extensive nor intensive than necessary, in the light of current technology, to detect the presence of weapons or explosives [and] that it is confined in good faith to that purpose.”So the key to the current set of procedures, in regards to the full-body scanners and enhanced pat-downs, is whether or not these tools are "more extensive" or "more intensive than necessary under the circumstances."
It seems to me that you could argue that in some specific cases, the procedures used by the TSA may have crossed this line (and in fact, they've more-or-less admitted this is the case in some cases); but there might be some difficulty arguing that these procedures in general cross the line (especially with the current Court).
Here is the text of the decision in its entirety: