The idea that most politicians are just empty shells that do whatever their funders tell them is just wrong. The truth is that it's cheaper and much more effective for funders to give money to politicians that already support their positions.
Lessig believes that if big money is taken out of politics that politicians will suddenly vote for fixing climate change, pass gun control, etc. But they wont because the ones that are against these things aren't against them because they are told to be, they are against them because they genuinely believe that they are bad policies. It's ideology, not money, that drives them.