The trigger is the Reagan shooting of 1981, compounded by Secretary of State Haig's now infamous statement that he's "in control" of the government. Haig was not only wrong constitutionally - a couple of elected officials stand between the VP and Secretary of State in succession to the Presidency - but his clumsy statement gives the Soviets the wrong idea that there may be a coup underway in the USA, which would prompt the Soviet Union to take some sort of military action to protect its interests.
There is a fearful, perfectly portrayed symmetry between the Soviet and American agents and how they each work on their own to stop this dangerous escalation. Phillip is the first to see that there may not be a coup going on here at all. Though he and Elizabeth have been here the same amount of time, he is much more perceptive about American political culture than is she. Elizabeth therefore at first opposes Phillip - and indeed kills a security guard in one of their surveillance missions - but one of the best parts of this series is how to the two come to reach conclusions through and in spite of their different starting points. The fact that Elizabeth is now falling in love with her husband, after all of these years, also helps - and is a good motive point in the plot.
Meanwhile, Stan uses his own contact with Soviets to get a handle on how the Soviets are reacting, and is able to convey to his superiors that no massive military action is imminent or even under planning. And, then, in a sweet move for the relative peace of the world, he tells his neighbors that American intelligence knows the KGB was not behind the assassination attempt. Since his neighbors just happen to be Phillip and Elizabeth, this is the final defusing element in the story.
As I've written earlier, Stan being the neighbor of Elizabeth and Phillip is the one conceit of the plot set-up which seems unlikely. But it was worked to great effect in this episode, and I'm looking forward more than ever to what may come next.
See also The Americans: True and Deep