This story largely ignores the fact that general-aviation operators pay quite substantial fuel taxes that actually pay for much of the government services cited.
Private aircraft do not need the large, complex, expensive airports that the airlines do, and they do not require air-traffic-control services to the same degree, either.
In fact, the air-traffic-control system, with its around-the-clock staffing, federal bureaucracy, radar installations, and extensive navigational system, was created for the airlines. It is sometimes forced on pilots of smaller planes, although some use it by choice. In any event, they pay for it with fuel taxes, whether they use it or not.
Many of those small airport provide valuable services to outlying communities, with emergency services, parcel delivery, and more personal transportation.
In addition, the local airports collect money through additional fuel taxes or profits, landing fees, ramp fees, parking fees, tie-down fees, and other charges. Some airports are profit centers for their municipalities, and they also support many businesses, even though the communities are often unaware of them.
The call for aviation user fees (which would created a much more complex system of payment than fuel taxes and require a new bureaucracy) has been prompted by the same airlines that have paid their executives huge bonuses while demanding major salary cuts from rank-and-file workers as a way to further get others to pay those executives' salaries. They have have gotten away with mismanaging their own companies and profiting from it for so long that they think they can get away with pulling the same scam on the larger public.
If you dig deeper into this issue, I'm sure you will see it for the boondoggle it is.