Very little. Will run off a dry battery for a few hours. Or maybe, "How long is your piece of string?"
Well, the Amps are low, but i belive most neon wire, as cold cathodes, use a high voltage. That way the electricty can bridge the gap from the anode to the cathode.
It's the surface area that matters, EL material also comes in tape and sheet form, as well as wire. If you want anything more complex than the common '12V inverter and 3m length of wire' complete kit, you need to be checking the suppliers.