When selecting a Facebook page to connect to a NationBuilder broadcaster, it seems that all pages that the control panel user can access on Facebook as an admin should be displayed. However, there is a report of this selection being limited to 22 options (the user reporting this is a Facebook admin of over 70).
This is the first time we've ever heard of anyone running into this problem. If you are experiencing this issue please add a comment so we can understand how regularly this happens.
As a workaround, have another admin of the page with less pages connected to their Facebook account connect the page to the Broadcaster.