UPDATE: There is an Update in the App Store that will fix the iOS7 compatibilty problems!
Anyone that upgrades their iPad or iPhone to iOS7 will lose access to any books they were reading.
The immediate remedy is to uninstall and re-install the Overdrive app which will also require you to re-authorize with Adobe. IMPORTANT NOTE: A re-install will clear a user’s bookshelf, history, and app settings.
Refer to the iOS section of this Help article for assistance.