LocalStorage is hard limited to 5MB in most browsers because it's not intended to be a large db.  IndexedDB is a Final Call Working Draft now and is usually 50MB+ (and can grow), but support for it is still limited (Chrome, Firefox, IE10, no Safari/iOS).

My gut tells me that storing the data server-side and just giving somebody a cookie associated with a non-OpenID account (as Phil describes) is probably the way to go.  I don't know if you want to store data saved this way indefinitely or clean it up after a period of time though.