Remember what goes on at airport checkpoints is an administrative search. While it might carry a civil penalty there is nothing illegal about refusing an additional search.

A LEO (probably several) will undoubtedly be called, run a NCIC check, interrogate you and possibly perform a criminal frisk (which is less objectionable than the TSA version). Ultimately if you continue to refuse they will eventually let you leave.

There's a thread on here somewhere in which someone did exactly that.

IANAL