I like Facebook, not only for supporting an organization but for other things as well. My family is rather large and scattered all over the United States. We set up a private group on Facebook and used it to communicate to everyone about the dates of the reunion, what everyone needed to bring, and as a forum to discuss things. It worked SO well, allowing everyone to get everything worked out and settled before the big event. My sister saw a bad ambulance service situation in Cedar County, Missouri, and used Facebook to relay the facts and rally her friends in reforming the service and making it better for the citizens of the county. It worked! I know my sister, and if she stands up for something, it gets done. Facebook just made it easier for her.
Organizational support on Facebook would be no different than going door to door, putting up flyers or posters, or going before a television camera. It's just a different type of medium to get your point across, get support, and rally the troops!