Let's say there is a better Iraqi military performance during the Gulf War. You don't even need to have an Iraqi invade SaudI Arabia during this stage, suppose the following happens:
* The Iraqi Air Force stays and fights rather than flees to Iran, confronting Coalition aircraft and perhaps conducting a few air to ground missions. Maybe even anti ship missions in an attemot to repeat the USS Stark affair.
* Scud missiles are used against Coalition bases rather than a futile attempt to draw Israel into the war.
* The Iraqi Navy heavily mines Kuwaiti waters.
* Iraqi ground forces take sensible steps like laying plenty of mines, oreparing dug-in positions and fortifications for tanks, artillery, and infantry, setting up ambush positions, and deploying forward scouts, sentries, and artillery spotters and conducting patrols to ensure they aren't taken by surprise, which results in more hard-fought battles such as Medina Ridge. Kuwait International Airport, and Phase Line Bullet.
* The Iraqis don't flee Kuwait en masse, forcing the Coalition to fight it's way through and take Kuwait City in fierce house-to-house fighting.
I think the Iraqis could reasonably have inflicted enough losses on the Coalition that, while not changing the final outcone, wouldn't be quite so lopsided. Also, this would have ramifications foreign policy wise, especially when it comes to the question of the no fly zones or whether or not to invade Iraq later.