You do not know how US politic work did you?
Look at it this way, if we stress too carefully on those petition and alter our policy to fine tuned to those people who signed the petition, then some other group will be ignored by our new policy and they will start another petition. It's will be endless cycle of just reading/reacting to petition, which our country will not do much.
The unique states in America is, we do not need to satisify all the people like a uniliteral government, we only need to swing into the MAJORITY of the American. When the intensity of citizenery dissatisifory level increase, then we will need to adjust our policy, not whenever people sign some petition, that's a very big different.
Petition itself is useless, it just show you some portion of your people do not satisified your policy, but you know there are always people that feel left out or don't agree on the government on some point, do we need to care everytime? NO, because whatever we do, we will just be able to please one portion of the people, the other part will just start and sign another petition, and i am pretty sure our government exist is NOT ONLY for responsing to those petition.