If you quite shortly after getting GC stamp, INS may withdraw your GC. This is how they may come to know :
1. You employer can ask INS to cancel your GC because quitting right after getting stamp indicates that you did not have intent to work for this employer permanently (INS calls it fraud).
2. If above does not happen and suppose INS never knows about your quitting, there is another way for INS to find out. When you apply for citizenship, INS goes through your past immigration history, they might notice it and raise questions and if not satisfied, they may cancel your GC.
Play safe, don't quit before atleast six months . Although nobody has defined meaning of "permanent" but most people think that staying 6 months to 1 year is safe. If current employer lays you off due to financial/business reasons, you will be ok.