They will insist on diplomatic negotiations. If Sadam plays it smart, he can gain a lot in exchange for a withdrawl from the occupied Saudi Arabian east coast. All the while negotiating under the political protection of the USSR. The early 80 's were one of the coldest periods in the cold war. Only for that reason the USSR will likely put their heels in the sand in this case. After OTL's invasion of Kuwait president Bush still insisted on a fiat of Gorbachew for a militairy intervention.
Different situation. The First Gulf War only involved Iraq seizing Kuwait. Seizing the Saudi Arabian oil fields is far, far, far more provocative than seizing Kuwait. (Saudi Arabia having double the oil reserves of Kuwait.) The U.S. might tolerate the annexation of Kuwait under the right circumstances, but it would never stand for a hostile power seizing the Saudi oil fields. Indeed it would be safe to say that the US's biggest three red lines during the late Cold War (the lines for which the United States would absolutely be willing to fight World War 3) were:
1) Invading the United States;
2) Invading Western Europe and/or Canada;
3) Invading Saudi Arabia.
So while the US might negotiate with Saddam (if for no other reason than that it will take time to move III Corps to the Middle East) those negotiations will only last until the heavy divisions are in place. Then if Saddam is still in Saudi Arabia the US will attack.
Furthermore, the Soviets know this. They get that Saudi Arabian oil is absolutely vital to the Western worlds economy and thus that the US will definitely fight to keep that oil out of Saddam's hands. The Soviets also know that they don't have any vital interests at stake. They aren't bound to Saddam by any treaty obligations, his continued existence (let alone his conquests) aren't important to Soviet security, and they don't need Middle East oil for anything. Thus with them knowing that the US absolutely will fight to eject Saddam from Saudi Arabia and with them having absolutely nothing vital at stake, there is no way the Soviets put their heels in the sand. The Soviet leadership is not suicidal and will not sacrifice Moscow for Saddam.