The Saudis that were shitting their pants that they were going to be next after Kuwait.
The Saudis were going to be next after Kuwait - Iraq had already taken territory across the border when the US entered.
The invasion was caused by the other Arabs attempting to jew Saddam and Saddam was just exploring alternative methods of repaying his war debt.
The Iran-Iraq war is a 'modern' lesson in mismanagement of a war, mainly due to the fact that the officers and armies involved were Arab (cry me a river about how you're "persian", if you worship the child-fucking prophet and live in the desert, you are a sand nigger Arab). Anyway, its a fun read (especially the part about how Iran has more F-14 Aces than the US) but Saddam through most of the 80s was viewed as the savior of the Sunni Arabs against Shiite aggression, and the Iraq war machine was largely bankrolled by Saudi Arabia, Kuwait, Qatar, UAE, and Jordan to try to take down a newly aggressive post-revolution Iran least the rest of the Shiites start getting ideas.
When the UN sanctions to try to end the Iran-Iraq slapfight came down, it left Saddam deeply in debt and having trouble being able to meet its loan repayments. SA and Kuwait were happily twisting the knife they'd buried in his back by raking his balls over the coals on repayment terms. Now, part of this was Saddam's own goddamn fault - fucker was building gold palaces after all - but while Kuwait and SA didn't deserve to be thrown out of a 2nd story window, they also shouldn't have give Saddam Wallace's wife a foot massage. They'd encouraged the war for a long time, and now they wanted Iraq to disarm because of the fear that he'd set his sights on lands to the west and south. Fears that turned out to be justified.
It occurred to Saddam that it would be cheaper to just invade the countries he owed money to and eliminate his debt that way - he had a shit load of trained conscripts and depreciated military gear, after all. Its not entirely clear what his plans were - it seems likely he wanted to annex Kuwait (and their oil/wealth) wholesale, but Saudi Arabia is less clear. Saddam viewed himself as the rightful leader of all Arabs, but probably couldn't have kept Saudi Arabia - and nothing on the Iraq-SA border is worth taking. The analysis I read said it was likely he just wanted to force them to surrender, and forgive Iraq's debt from the Iran-Iraq war. But its Saddam and he was pretty unstable at this point, so who the fuck knows.