Lessig comes so close to seeing that the democratic legitimacy of the Republic is a sham. As a big-shot talking to a bunch of other big-shots, it's understandable that he would think that the system is ultimately responsive to the people.
"Fixing the problem" is not impossible, but his strategy is a non-starter. A broken system cannot fix itself. The law-making process cannot be fixed by passing a law.
He's trying to be radical, but he stops short. His analysis is superficial -- the thinks that the problem is in how money is obtained, but he doesn't ask why money is necessary. He doesn't answer this question, and therefore he doesn't realize how detached regular people are from the rule making process. He doesn't realize that the system is elitist (and "corrupt") at its core.