There's a lot of outrage over the possibility that John Tyner could be fined for refusing to either go through the body image scanner or be subject to an invasive frisk, but the courts have traditionally been very deferential to the government when it comes to airport security.
In the 1970s, there were a number of cases that basically established some very government-friendly precedents. For example, in United States v. Davis, the court found that airport searches are constitutional, but only if you have a right to refuse them:
One important caveat should be stressed, however. To meet the test of reasonableness, an administrative screening search must be as limited in its intrusiveness as is consistent with satisfaction of the administrative need that justifies it. It follows that airport screening searches are valid only if they recognize the right of a person to avoid search by electing not to board the aircraft.
Now that sounds pretty reasonable right? And in Tyner's case, the government would seem to be overreaching, because even if someone has a "right" to refuse, that hefty $10,000 fine basically means you won't. But later the courts basically established something like that was OK too, in order to avoid "mischief":
In Skipwith we also dispensed with any notion that a traveler can attempt to enter the secure area and then beat a retreat if the search proves not to his liking. "Such an option would constitute a one-way street for the benefit of a party planning airport mischief, since there is no guarantee that if he were allowed to leave he might not return and be more successful." We noted that an unimpeded exit would diminish the risk to skyjackers and increase attempts. Established search procedures are more valuable for what they discourage than what they discover, and this court in Skipwith saw no constitutional reason to afford a "heads-I-win, tails-you-lose" guarantee to criminals wishing to board aircraft.
So some activist judge is probably not going to declare the searches or the body scanners unconstitutional, and there's no clear legal avenue to getting rid of the punitive fines either. So if you want less invasive security procedures, it's going to have to get done the old-fashioned way, through legislating.