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In my experience, the only way to get things done is to appoint, elect or volunteer a project manager to oversee everything.
You then need to create a project plan, with target dates and deliverables. The overall goal is to break the larger deliverable (i.e., the petition), into smaller pieces that can be worked on by small groups or individuals, and that can be more easily tracked.
While there is science behind project management, there is also art and creativity (which is why, in reality, most projects fail – either they run horribly over deadlines, or horribly over budget, or never complete at all).