The problem with money in politics is only incidental. As long as we allow politicians enormous and ever-increasing power to pick winners and losers and grant special favors to friends and interest groups, the money will keep flowing into the system. Money flows to power (as long as it remains a good investment). The problem is the unrestrained power, not the money.
I'm not sure you can legislate "unrestrained power". You can however make it "painfully illegal" to input any form of money into the politic process. You have a choice to start at either end of the problem. I think the only viable solution is where Lessig is heading: remove all the money from the process. Not easy, but achievable. Going at it from the "power end"?? I have no idea how to start with that considering the U.S. Constitution already provides the best known 3-way power infrastructure.
The US Constitution was designed to restrain the power of politicians. The problem is that we don't follow it. And unsurprisingly, the more discretionary power that politicians accumulate, the more money flows into the political system despite all number of laws such as McCain-Feingold. Similar to nearly all regulations, campaign finance laws have the effect of excluding small players from the system entirely and benefiting large players and incumbents who can front the compliance costs and reap sufficient benefits from the system to overcome any hurdle.
For an entertaining introduction to the effect of unintended consequences on campaign finance reform, watch John Stossel's Politically Incorrect Guide to Politics, part 4:
Why not do both? Why not reduce their power some, change the law to reduce the variability of money in the system and see what happens? It doesn't have to be either/or.
This constant argument that we have to do A only, followed by the counter-argument that we have to do B only, seems to come more from our love of arguing and being righteous in some stance than from common sense consensus-building or the urgency of experimentation and progress.
