I had this problem on my 2002 Impala. I scanned it and the scanner showed had a miss-fire on the number one cylinder. This was not the issue. The catalytic converter was bad, the front portion of it had broken internally and partially logged the exhaust port. Chevrolet has a service bulletin on this, if you car is included they will replace the converter free of charge. This could or could not be your problem, but it was what was wrong with my car. As usu-all GM will have a service bulletin on known issues rather than a recall, that was you may or may not bring them the vehicle, thus they may or may not have to fix it.