There is already a federal 9/11 security fee. It is "used to pay the government's cost for providing Federal civil aviation security services. This includes training, salaries, and benefits for the Federal security screeners and law enforcement personnel, as well as the Federal Air Marshal program."
FFDO falls under the FAM program.
So you see, airlines (via their passengers) are ALREADY paying for the FFDO program.
Also, for all the talk of "we're broke", I still haven't seen the OP discuss VALUE. The cost vs. benefits of FFDOs vs. FAM, TSA, or any other security function. Or DETERRENCE.
If one draws a conclusion that "No FFDO has used their gun to defend the flight deck, therefore FFDO is an unnecessary program", one can just as easily draw the conclusion that "There have not been any hijackings since FFDO was implemented, therefore it has been a completely effective deterrent."