The current "We the People" website merely requires 25,000 signatures of a populate of roughly 350 million. Having 25,000 signatures of this population size is statistical noise, and it offers no mechanism for people opposed to any given petition to have their say.
Every petition ought to have the ability to sign for or against the proposal. Then, only after a minimum total signatures has been met, and the ratio of signatures for, rather than against the proposal is greater by a significant margin (say 4:3), should it be considered.