Neil Armstrong steps out of the lunar lander but instead of the words we are familiar with he says this, "Hey Houston, I've got two words for ya. We defect!" He then unfurls a Soviet flag the astronauts somehow smuggled on board, and starts singing the Soviet national anthem.
All three astronauts are defecting to the Soviet Union. They intend to land in the ocean near by the Soviet Union or a nation friendly to them and defect as well as giving the soviets the space capsule.
While they are in space I don't see what the US can do about them. When they return I would guess the US would try to intercept them before the Soviets get to them. This could turn into a nasty stand off between both countries if they both arrive in the area at the same time.
First what do you think the first words to come out of Nixon's mouth would be when he sees it?
Second what do you think the repercussions would be when they return, both long term and short term?