I'm having the same problem with my 97 Lumina! It started out with the left turn signal not wanting to work (or working intermittently), then the right...now neither of them work - I have to hold down the arm until just BEFORE it clicks to get it to flash - otherwise it won't work at all if you click it down all the way.
I had my mechanic look at it and he said to fix them is about $200! Are the parts cheaper if you do it yourself??