I'm on an iPhone 5, iOS 6.1, with the newest Spotify version.
I am unable to sync any music of any kind. The circular progress icon just keeps spinning, and never stops. This is not for local files, but music on Spotify.
I uninstalled Spotify, and reinstalled it. Selected "Available Offline" on my Starred playlist, and it syncs all the songs currently in the playlist. As soon as I add a new song, it just hangs.
Also, I don't have over 3,000 files stored, much less than that.