There was an episode of The Outer Limits that I remember, where there was at least one alien ship landing on Earth, and there were several bunkers with a single person inside who had to keep entering a code (or pushing a button) to stop from destroying the world.
This is "Dead Man's Switch", Season 3, Episode 13, of the 1995 series.
A fleet of alien spaceships are seen heading toward Earth. Knowing they might be evil, a Doomsday plan with a Dead Man's Switch is prepared, with five people in individual bunkers sharing the responsibility to prevent the doomsday plan from being enacted (should it become unnecessary) by regularly pressing a button to keep the doomsday device from turning on. The five people in the bunkers are gradually killed off in a variety of ways. The brief hope for peace is extinguished when a second fleet of colonization ships is found and the button pressers lose all contact. They die in their separate bunkers one by one until the last one remains. He finally decides to let it happen when he gets a message from his commander telling him they defeated the aliens with a new weapon. He stops the Doomsday Device at the last second and is told to keep pushing the button until they can disarm it.
The last scene shows the aliens who used the commander as a puppet, eating his brains over the glowing red ruins of Washington DC.
Found with a search for
"outer limits" "push * button"