If you are looking for an open source stack looking to solve a similiar problem, you might want to keep an eye on PouchDB (http://pouchdb.com) as well as CouchDB / TouchDB. (disclaimer, one of the PouchDB authors)

It is nowhere as near as 'out of the box' as firebase is, but every part of the stack is open and I dont think it will take a long time until it is as ready out of the box as firebase is.