Making connections on Facebook is not limited to friends. Through both Facebook Pages and Facebook Groups, you can stay more connected with everything that matters in your life—from businesses and public figures to common interests and hobbies.
To increase the likes on a page one way is to do targeted promotion with a small budget. (Start by target people who live in the local area who are interested in politics)
Another is though sharing posts although it is not much use say me sharing anything as I have no local people that are friends.
So we need each person who has local friends and is a branch member to like the page and share a post created about the group.
To forge these ties on Facebook, it's important to understand the difference between Facebook Pages and Facebook Groups.
Even though you have a page – at some point there may be a case to make a group the difference being:
Like a friend's profile, Facebook Pages enable public figures, businesses, organizations and other entities to create an authentic and public presence on Facebook. Unlike your profile, Facebook Pages are visible to everyone on the internet by default. You, and every person on Facebook, can connect with these Pages by becoming a fan and then receive their updates in your News Feed and interact with them.
While Pages were designed to be the official profiles for entities, such as celebrities, brands or businesses, Facebook Groups are the place for small group communication and for people to share their common interests and express their opinion. Groups allow people to come together around a common cause, issue or activity to organize, express objectives, discuss issues, post photos and share related content.
The other thing is you can’t pay to promote groups – so you use a page in conjunction with a group so it can be promoted to potential members