I can agree with that partially. Petitions CAN sway local government. And local government has the power to sway state and federal government. I just don't think Congressmen pay attention to petitions. Perhaps if they come from their home state, but that's it.
"I just don't think Congressmen pay attention to petitions"
I don't mean the type of petition where many people sign the same letter. I meant where everyone mails in thousands and thousands of individual signed letters. Dump bags of letters into each office. I think it would get some attention.