I've always felt petitions were used by lawmakers to help filter noise. If you set a threshold for the amount of support any cause needs before you'll address it (preventing you from having to listen to each person individually) the petition system seems only logical. If the lawmakers now see that 100,000+ people are against their decisions they promised to make a response but have no obligation to change anything.
This is where people's voting power is supposed to matter. If the representatives are always ignoring the issues that are deemed important by petition/protest groups then why should the be expected to get re-election?
Its sort of a shit deal where we're hoping the channels they provide will show some benefit or marshal of change but I haven't seen that happen yet. I'm not American so I'm somewhat distanced from everything but it has always seemed like these petitions were just another campaign tool and never intended to be taken seriously by gov't.