Have you been involved in a legislative process? (I haven't, directly, at the federal level.) At the local and state levels, hard petitions are huge. (In some jurisdictions, they're required to get on the ballot.) Protests are meaningful inasmuch as they are willing to show up, time and again.

Why? Off-season elections, which most of these politicos must win to keep office, are not games for numbers. They're games to motivate people to inconvenience themselves by voting.

Remember why politicians like PAC and campaign contributions. They spend that money on turning out voters. If you can turn out a bloc of potential voters, or people whom you can reasonably claim are upset enough to vote against them, you'll catch attention. The active minority wins against the disinterested majority. Internet petitions represent the latter; hard petitions and protests high in repeat attendance demonstrate the former.