humm... i wouldn't think its your transmission at all... you see, if it were, your engine would revv up, but the car wouldn't move for a sec or two.
I take it your Saturn is Fuel injected?... if so, getting the injectors cleaned (or putting some gas treatment in) may help.
Also, if it is F.I., you probably won't really be able to flood the engine like you would with carbs.
Check your air filter... if its really dirty, it may be restricting your airflow, and then causing your engine to flood.
How long has this been happening?... if not too long, it may be just a bad tank of gas.
Like the mechanic said though, i would really check into the fuel and air systems. you may even have a cut fuel hose, allowing air into the line, and that may be causing the semi-stalling.
About the transmission jerking off
... I know all Hondas shift hard. If your car didn't shift hard at first, but is now, you may have a problem. If it's always shifted hard, it may just be normal for that car.