I like how it's a little "off" throughout. For example, the weather changes in unusual ways during his journey. For most of the story what's "real" or not is up in the air, but Cheever doesn't make a big deal of it.
But the reveal at the end still gets me, when we realize dude's been fooling nobody but himself.
I feel bad for him. I think the insanity that comes from trying to save social face is understandable and common. I get the hesitation to care too much about this high-middle-class guy, but when I look beyond that, I can see something like this story taking place in an African village or something.
Burt Lancaster starred in a movie based on the story:
http://www.youtube.com/watch?v=yIegoQAayFs
And here's a cameo from Cheever himself:
http://www.youtube.com/watch?v=TZGQzUsnPqo