In my home town, we had a local group of mostly old folks, largely right-wing, who would have monthly luncheons with local politicians, and the group was literally called the Phone Tree because that’s how they organized. Although in this case the “Phone Tree” was a primitive robodialer owned by the head of the organization and used to disseminate recorded announcements of when the next luncheon was and who would be the guest/s.
The machine was literally called a "Phone Tree". Presumably because it was intended as an automated replacement for an old-fashioned phone tree. And, back to the root point, telephony can be used to organize political activity, at least in the form of getting all the old gun nuts in town to show up for a luncheon with their state legislator.
And pretty bad at doing it. It's actually pretty funny to imagine someone trying to organize a movement via a phone tree.