The Iraqi army, with a core of battle-hardened veterans from the just-finished Iran-Iraq war, although paltry by world standards, is able to brush aside the even more paltry Saudis, despite their latest equipment.
When word gets out that King Fahd & the Saudi Royal family has fled to France, resistance collapses.
Jordan, Lebanon and Israel, with large Palestinan pro-Saddam minorities, are destabilised, Hussein being viewed as some kind of Islamic Messiah/5th Imam. Even the Iranians look on in admiration.
The conquest of the Saudi & Kuwaiti oil fields is so quick, and with the prospect of 30% of the world's oil being destroyed in the event of a US-led invasion, Bush weighs a nuclear decapitation of Saddam in Baghdad. But Bush is no Reagan and backs off.
Gloating over his conquest, Hussein loses interest in firing Scuds on Israel.
But the US quickly plots to use Israel, the only ones who could get away with it and refocus the Arab world at the same time, as a tool to take out Saddam with a 'false flag' operation. Israeli micro and mini nukes get to be used. The world gets to see what an above-ground 0.01 kT atom bomb explosion looks like.

(PS: Should the Moderator intend to lock this, before doing so, could he please explain if and where it is deficient in POD or POV, to give me a chance to amend it!).