Honestly, I've seen the "gummy rubber" symptom most commonly on roller-drive turntables when the pinch-rollers got sticky. Those containing pinch-rollers are usually not really quality tables, so if it has a roller-drive, I probably wouldn't mess with it. But if it's a nice turntable and it has just gotten dirty, then cleaning might take care of it.

One last thing about solvents. Do be careful what you use to clean with. If you find rubber deposits on a pulley, there's a good chance that whatever rubber wore off on the pulley is pretty well decomposed. So you may need a belt or pinch-roller anyway. But be careful with stuff like alcohol and other solvents. It will clean that metal pulley nicely, but it might turn any rubber it comes in contact with into gummy bears.