The catch, of course, would be that the PPA would have to make up the money by raising the tax rate above the normal level in economic good times. But that might have a salutary effect too--averting inflation by cooling down an overheated economy, much the way a Fed rate increase does.
Won't there be huge pressure on the PPA to keep priming the pump and never make up the shortfall? Sure--just as there's pressure on the Fed to keep cutting interest rates. But the Fed usually manages to resist those pressures, and you could design a PPA so it had a similar ability. (The usual technique involves appointing its members for fixed, overlapping terms, and bringing the weight of sober, prudent business opinion to bear on the President at appointment time.) Even elected officials--presidents, at least--would have an incentive to restrain irresponsible pro-stimulus impulses. They want to be seen as fighting unemployment, but they've also learned that inflation is electoral poison. And not only in the long run. Ask Jimmy Carter.
You could have the Fed itself be the PPA, though I assume there are arguments against giving too much power to one agency. Those are arguments we should maybe have, because what's "fast-moving" for Congress is too slow.
Another country is complaining about an influx of Mexicans crossing its borders looking for work. That country is Mexico. From the Tucson Citizen:
Sonora - Arizona's southern neighbor, made up of mostly small towns - cannot handle the demand for housing, jobs and schools it will face as illegal Mexican workers here return to their hometowns without jobs or money.