Operation Desert Storm, or the First Gulf War, was a war fought between 1990 and 1991 between Iraq and a coalition of 35 nations authorized by the UN. The United States was the main member of this coalition. The purpose of the war was to liberate Kuwait from Iraqi rule after Saddam Hussein invaded.
When Nick wakes up in the hotel room shortly after the sex hallucination, a news show on his tv can be heard. On it, the anchor says "The US Congress said today that the bombing of Baghdad will continue until all Iraqi forces have pulled back across the Kuwaiti border."