is it an analogy?
Perhaps anticipation of the consequences of a President’s death should be obligatory for Vice Presidents, but it wouldn't come easily. There is little evidence that Johnson s seven predecessors had given the matter much thought. The attitude of national politicians toward the White House is highly ambivalent; they simultaneously crave it and recoil from it. Vice Presidents, like Presidents, are loath to dwell upon the fact that they are a heartbeat away from the executive mansion, and when the beat suddenly stops they are dumfounded. "I don't know if any of you fellows ever had a load of hay or a bull fall on him.” Truman told reporters on April 14, 1945, "but last night the whole weight of the moon and stars fell on me."]

what does "the beat suddenly stops"mean?

Question

is it an analogy?
Perhaps anticipation of the consequences of a President’s death should be obligatory for Vice Presidents, but it wouldn't come easily. There is little evidence that Johnson s seven predecessors had given the matter much thought. The attitude of national politicians toward the White House is highly ambivalent; they simultaneously crave it and recoil from it. Vice Presidents, like Presidents, are loath to dwell upon the fact that they are a heartbeat away from the executive mansion, and when the beat suddenly stops they are dumfounded. "I don't know if any of you fellows ever had a load of hay or a bull fall on him.” Truman told reporters on April 14, 1945, "but last night the whole weight of the moon and stars fell on me."]

what does "the beat suddenly stops"mean?

Answer

Although all vice presidents know that this is a possibility, but when it actually happens to them, they are dumbfounded.

Answer

"A heartbeat away from the executive mansion (presidency)" is a phrase meaning that the vice president is literally one heartbeat away from becoming president.  The moment the beat (heartbeat) of the president stops and he dies, the vice president becomes the president.   Although all vice presidents know that this is a possibility, but when it actually happens to them, they are the are dumbfounded.

Answer

'a heartbeat away' is a figure of speech (Synecdoche?), not an analogy.  It denotes 'life' in this context; in other contexts it denotes a short time, less than a second.  As your other reply said, 'beat' is the 'heartbeat'

Answer

The "beat" here refers to the heartbeat in the previous clause. It means "when the heartbeat stops", or, when the President dies.

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