(My guess is "yes", because that is how the US federal government works. If there is not extremely strong wording saying something is your right in the Constitution, it's not. Of course, there is explicit wording along the lines of "The powers not delegated to the United States by the Constitution, nor prohibited by it to the States, are reserved to the States respectively, or to the people," but that's a little too broad for lawmakers or the Supreme Court to understand.)
A frequent flyer friend of mine suggested the naked airline. Basically you take nothing on board, get shoved in a box, but you get to avoid the TSA. The funny thing is he thought dealing with the TSA would be the hardest part of getting this off the ground. I often wonder how many other flyers would find this reasonable.
IANAL