Airports have already privatized some terminal security agencies. At large airports the TSA will most always be there but at smaller more remote ones they have private agencies overseeing the duties the TSA would normally provide.
I am assuming you meant the TSA as "a whole" becoming privatized. What would probably happen is that they would become subsidized by the government and still owned by them in a sense. So nothing would probably change and employees would probably get worse because they no longer would have to undergo as harsh of an interview process because they would not be applying for a government job (If you have been to a private jail or prison you have seen for yourself).
We can continue to create a discussion by once again assuming you meant something different and maybe what you meant was the creation of a "private" organization serving the duties a TSA agent would but separate from the government. Are we willing to deflect the responsibility of security clearance to another agency and CONTINUE to allow the invasion of privacy? Is there another solution?
That is my question, is there another solution? One that will provide protection for intra- & inter- continental travel...Maybe it is something I will explore myself in my endeavors.