You may need to click “Refresh my contacts” under Preferences and allow the app to search your phone for matched contacts. It may take the app several hours/days to find matched contacts, so check back from time to time.
This action is similar to "Invite Your Friends," but you are limited to sending invites only to contacts the system has matched (e.g. a voter universe) to provide a special invite.
Note: Matches aren't guaranteed.