To be fair to Lessig, if the single issue "pass this bill" candidate was actually elected President, congress would feel a lot of pressure to comply.
Yes, but Presidents aren't elected by majority vote of voters in a majority of Congressional Districts. That's especially true of Democratic candidates, who tend to be hyperconcentrated in urban districts (in part, gerrymandering, but in part that's just the geographic distribution of Democratic support and why even without state-size biases and gerrymandering, Democrats are structurally disadvantaged by single-member, FPTP representation in Congress.)
I just don't see it that way at all. Think about Obama's work on national health care. A ton of democrats were worried about supporting it.