There were a number of factors that contributed to the USSR's acquiescence and support of the various UN resolutions to evict Iraq from Kuwait.

Firstly, the dominant buzzword surrounding Soviet foreign policy during the late Gorbachev era was "New Thinking." The central idea animating this concept was that the post-89 Soviet state should foster a constructive relationship with the United States and European community. This meant a reversal of the Soviet UN Cold War strategy of using the institution either to symbolically harangue its opponents or threaten to employ its Security Council council veto as a means to block action. Iraq's invasion fit very well into this paradigm as it provided an opportunity to show that the superpowers could form a constructive relationship and that the opinion of the USSR still mattered in world affairs. A veto would have escalated tensions with the US when Gorbachev wanted them eased.

Although some Western commentators thought New Thinking was part of a wider trend in Soviet politics, it was quite controversial within the Soviet government. Some Soviet hawks were alarmed at the loss of Soviet influence over events once the UN sanctioned the US-led Coalition. This dovetailed with wider domestic problems and discontent within Gorbachev's government. The Gulf crisis coincided with the beginnings of the breakup of the Soviet Union, with independence demonstrations in the Baltics and Georgia. These domestic problems not only hamstrung the hawks from acting more forcefully, but it also distracted the Soviet government from playing a more active role. The Soviet reaction to the Primakov mission reflects the divided nature of the Soviet foreign policy establishment at this time. Yevgeny Primakov, a member of the Presidential Council, went to Baghdad as a special envoy in October 1990 and hoped to convince Saddam to evacuate Kuwait in exchange for oil fields and an international conference on the Palestinian question. The Soviet Foreign Minister Eduard Shevardnadze was furious about the Primakov mission as it usurped his authority and undermined his attempts to forge a working partnership with James Baker. Shevardnadze undermined Primakov's attempts at bilateral diplomacy by pushing Gorbachev to support the UN resolution authorizing the use of force. Shevardnadze's surprise resignation in December 1990 created even more confusion within the Soviet government as to how the handle the Gulf crisis. Primakov tried to prevent a ground invasion by traveling to Baghdad in February 1991, but by then it was much too late.

The fundamental problem Primakov faced was that Saddam was not a willing partner and often overestimated Iraq's clout in international affairs. The Kuwait invasion was a diplomatic blunder that openly transgressed international law in such a flagrant manner that it was difficult for any state to take Iraq's side. Kuwait was one of the more pro-Soviet states in the Gulf and Iraq's invasion shocked many in the Soviet government, including Gorbachev. As Saddam retrenched his position that the invasion was a fait accompli, it became harder for Iraq's previous partners to support it. The Iran-Iraq War had already greatly strained Iraq's relationship with the Soviet Union. Saddam tried to construct alternative networks for military equipment during this war from France, Yugoslavia, and China as a means to gain more favorable support from the Soviets. Transcripts of Saddam's foreign policy meetings show that he thought he was being clever by playing this gambit, but many within the USSR saw through this.The net result was that many within the Kremlin saw Saddam as an inconsistent and troublesome partner in 1990. The Soviets continued to support Saddam in the mid and late 1980s, supplying Scud missiles and advanced aircraft like the MiG-29 and Su-25, but the there was little love for Saddam among the Arabists in the Kremlin. Gorbachev's swift public denouncement of the Kuwaiti invasion laid out that the Soviets would not accept Iraqi wholesale occupation of Kuwait. The preferred course of action favored by the Soviets was a diplomatic one in which Iraq would voluntarily leave Kuwait after a face-saving gesture, but the Iraqis refused to acquiesce. Supporting UN resolutions was part of this Soviet strategy as it underscored the Soviet's fundamental position that the Kuwaiti invasion was a violation of international norms. The failure of Saddam to use the Soviets as an escape hatch meant that the Soviets lost a chance to impact the course of events after the January deadline.

Sources

Allison, Roy. Russia, the West, and Military Intervention. Oxford: Oxford University Press, 2013.

Andrew, Christopher M., and Vasili Mitrokhin. The World Was Going Our Way: The KGB and the Battle for the Third World. New York: Basic Books, 2005.

Ekedahl, Carolyn McGiffert, and Melvin A. Goodman. The Wars of Eduard Shevardnadze. University Park, Pa: Pennsylvania State University Press, 1997.

Grachev, A. S. Gorbachev's Gamble: Soviet Foreign Policy and the End of the Cold War. Cambridge: Polity, 2008.

PBS Frontline, "Interview with Mikhail Gorbachev," http://www.pbs.org/wgbh/pages/frontline/gulf/oral/gorbachev/1.html

Why would they? The US had largely replaced the Soviets as Iraq's benefactor in the 1980s (due to the Iran-Iraq War). The Cold War was over and the USSR was looking to get US aid, not to antagonize them.