Actually we have a historical precedent to what Chomsky describes. There has existed an institution that was designed more or less to tackle this kind of problems. It existed in the days of the Roman republic and it was known as the the Plebeian Assembly/Council of the plebs.
It was lead by the so called " Tribune of the plebs ". To Summarise his job:
Tribunus plebis, rendered in English as tribune of the plebs, tribune of the people, or plebeian tribune, was the first office of the Roman state that was open to the plebeians, and throughout the history of the Republic, the most important check on the power of the Roman senate and magistrates. These tribunes had the power to convene and preside over the Concilium Plebis, or people's assembly; to summon the senate; to propose legislation; and to intervene on behalf of plebeians in legal matters; but the most significant power of these tribunes was the power to veto the actions of the consuls(Well reads as senate) and other magistrates, thus protecting the interests of the plebeians as a class. The tribunes of the plebs were sacrosanct, meaning that any assault on their person was prohibited by law.
Also one important part is only Poor/Middle class could be a member of the Council of the plebs and Tribune of the plebs. Senators, Rich etc were not allowed to be members of the plebian council.
This institution held a significant amount of power along with the senate. It could even block Council elections under certain circumstances as the times of Ceasar ,Cisero, Pompey, Krassus, Cato etc show.
You can read about them on wiki: