The film takes place in a single day and night, beginning as the two main characters, Harry (Anthony Edwards) and Julie (Mare Winningham), meet at the La Brea Tar Pits and are immediately attracted to each other. They make a date for later in the evening, but fail to meet due to a quirk of fate. While they are apart, Harry receives a wrong-number phone call, and is told that, unbeknownst to everyone else, nuclear war is about to break out in fifty minutes. He searches frantically for Julie, helped and hindered by various strangers, who are initially unaware of the impending apocalypse. Some of the strangers they meet arrange for a helicopter to ferry a few to the airport, to catch a plane to Antarctica and safety. Harry makes arrangements with a pilot to meet them at the top of the building.
As the story reaches a climax, the news of the nuclear exchange breaks, and Los Angeles descends into violent chaos. Harry worries that he may be the cause of an unnecessary panic.
They reach the top of the building where the helicopter is supposed to be waiting to find the pad empty. After a missile streaks across the sky, confirming the war is real, the helicopter returns with the pilot badly wounded but fulfilling his promise to come back for them. After they lift off from the roof, three nuclear missiles hit L.A. and the EMP from the detonations causes the copter to crash into the La Brea Tar Pits.
As the copter sinks and the cabin fills with water, Harry tries to comfort Julie by saying someday they will be found and they will probably be put in a museum, or maybe they will take a direct hit and be turned into diamonds. Julie seems to take some hope in this, and the movie fades out as the water fills the compartment. A final explosion seems to imply a direct hit has taken place.