Hence the "at least no more than it's traditionally been". Money in politics is an important issue, but an old problem. It's certainly not any worse than it was in the 1890s or the 1920s.
Also, the problem Lessig raises is sort of weird from a democracy perspective as it arguably stems from too much free speech. That is, when speech is not free as in beer but is free as in freedom, in a market economy, the wealthiest speakers tend to crowd out the rest and disproportionately influence campaigns and politicians. So I'm not sure I'd file that as "democracy is dying" so much as "democracy is hard".
I think his argument is that it is worse today, largely because the cost of running a campaign has dramatically increased and that funding doesn't depend on the people, but on an extremely small subset.
Lawrence Lessig talks about it here: http://www.ted.com/talks/lawrence_lessig_we_the_people_and_t...