What could cause my steering wheel to wobble when I brake?

My friend said it could be my stabilizer bar or something. It only happens when I brake after going at a decent speed (normally on the highway going 50+ MPH). The steering wheel wobbles back and forth and sort of vibrates. It just happened the first time last night and scared the crap out of me. Also, if you suggest what it could be, please let me know about what I can expect to pay for it to be fixed. It's a 2003 Eclipse Spyder. Thanks!