Simple, Iraq seizes Kuwaït after detonating its first atomic bomb(s) and can blow up Ryiadh and Tel-Aviv, western opinions aren´t going to accept war with a nuclear power.
It is also made clear to Saoud Arabia that Iraq is ready to share much of the profit from the invasion of Kuwaït but also that allowing into arabian territories foreign forces will mean an all-out attack on its own oil facilities, followed by an all-out invasion and if it is defeated, a few dozens to hundreds of tonnes of VX gas (Saddam may or may not be bluffing whever he have these or not).
Thus, Saoud Arabia doesn´t want an attack from its own territories. A naval invasion of Kuwaït from sea would fail and starting from Turkey, the US would have to fight through Iraq itself, ditto for launching an attack from isreal through Jordania, it would alienate the US´s arabe allies.
Saddam Husseïn promises a Stalingrad scenario, in Kuwaït city, every building are linked by tunnels. Every door and house are booby trapped, western armies would have to destroy the city and effectively massacre most of its civilian population to liberate it.
The US starts upgrading the Saoudian military against an eventual Iraq attack, while Saddam Hussein races to construct more nuclear bombs and rockets.