Assuming the broken tip does not have a piece of the plunger in it, you may be able to use a reverse threaded screw (do they exist)?
Oddly, I did a little garage cleaning today and am now looking at a 4-way valve stem tool similar to this:
http://www.amazon.com/Milton-MILS-445-Steel-Plated-Valve-Repair/dp/B002XMSB90
Some claim the tapered end is just a tap, others say it can be used to remove a broken needle valve. I'm not sure which is true.
I also happen to have my camera out as I'm going on a day-trip tomorrow. The tip of the tapered end of the tool just fits into my cable-release (and I mean the end of the release, not the socket in the camera).
You may be able to use something like this to grab the broken part, and tilt the tool at an angle for enough pressure/friction to unscrew it. You would have to be very careful not to foul the threads of the socket.
The tool should be cheap, so a trip to your local auto parts store might be in order. Also, you could try to find a real hardware store - they may have a decent set of extractors.
Actually, perhaps you have a small drill bit that will fit in the hole. Even if not reverse-cut, you may be able to put enough pressure/friction by holding it at an angle to remove the tip. The shank may even work.