When the needle breaks off, it does not make sense to fix it, because you are basically going to have to strip down a working speedo to get a good shaft. Much easier and economical to replace the speedo head.
www.precisionpontiac.com will calibrate an lube a good working unit.
You are going to have to remove the dash, then take the gauge cluster out to get to the speedometer. Best to send one in, tell him what miles to put on the odometer, then when you take the dash apart, you have all the pieces ready to install so it does not sit for months, and the car is immobile.