Small Engines (Lawn Mowers, etc.): Briggs & Stratton 12.5 Twin runs rough, briggs stratton, fuel pump

Question
I have a Briggs 404437-0113-01 12.5 HP twin that runs very rough, RPM up and down.  I have tried adjusting the mixture screw (now out about 1-1/2 turns) and the idle screw to cure this problem and it is a little better but still the RPM still varies a lot.  The engine will run with the mixture screw all the way in.  Do you think I need to rebuild the carburetor and fuel pump, or is this a governor adjustment problem.  If you think it is the governor please explain how this should be adjusted.   
Thanks for any assistance you can provide
Al Piccotti

Answer
I need a little bit more information,  When you say Engine is running up and down, in the OPEC industry we call this "hunting and surging"  Is this what is happening?  When you pull the choke out does it level off?  Meaning does it then run smooth, please get back to me so i can help you further.

Dave