This represents a naive view of politics and political contributions. The simple part is that people, groups and corporations contribute to politicians (in most cases) because there is an advantage in doing so. There are sound economic reasons for doing this. The Federal Government controlled the spending of $3.7 Trillion last year. Through regulation and laws the federal government affected the creation, flow and expenditure of many trillions more dollars. All this "power" is concentrated in the hands of 535 Members of Congress (as well as a few thousand congressional staff), one President (as well as a few hundred White House staff) and a few hundred Federal Judges (as well as a thousand or so clerks).
The simple laws of economics dictate that these entities will get attention from the economy. In a sense, the political market is pricing the "fair value" of these positions far more accurately than their federal salaries price the "value" (impact might be a better word) in the economy at large. No law will change this as you cannot repeal the laws of economics. History has consigned a multitude of once great nations to the trash heap who thought they had transcended the laws of economics. There is no such thing. Pol Pot probably came the closest in creating a society transcending economics but the results were rather unpleasant.
If the goal is to reduce political spending, one must reduce the value of the politicians. To reduce the power of the politicians, one must reduce to power and scope of the federal government. No one would care to spend a billion dollars on a Presidential campaign or $40 Million on a Senate campaign if the federal government had less power to affect their lives, business or goals. Reduce the power of government and the political market will price these offices appropriately and campaign contributions will drop.
The failure of "political reformists" to recognize the problem is that government is too powerful and that the desire to influence this disproportionate power in society is why smart people contribute to politicians is testimony to reformists continued naiveté.
The advocacy of campaign finance reform by entrenched politicians who want the power of office without the hassle of well funded challengers represents the corruption of those "pretend reform" politicians as they are quite content to pretend to be angels in the view of the public and petty princes in private.
Anything less than reducing the scope of the all powerful, all encroaching, all taxing, all regulating, all spying, leviathan state is a childlike waste if time. Lawrence Lessig's proposal, no matter how well meaning, is no different.