Politics is about leverage. The more documentation there is that a legislative body's leader has willingly ignored his constituents' wishes, the easier it will be in the future to displace him. Politicians don't like being displaced.
Berger clearly enjoys being in power and may even run for a US Senate seat, etc. in the future. Imagine if we had 100,000 potential voters' signatures on the petition, or 1,000,000. Do you think he would just ignore that and still refuse to bring the bill to the floor? This is what I mean when I say that we as a group can work to get better leadership, whether that's in the form of actions from Berger or his eventual replacement. Nothing is guaranteed, but politicians respond to pressure all the time, provided that doing so is in their best interest.