What is a good short story about the american dream to compare with Arthur Miller's Death of a Salesman?
"The Secret Life of Walter Mitty" is a story about a person who escapes into fantasies in order to escape from the intolerable conditions of his dull life and his overbearing wife.
"Sonny's Blues" might be a different direction to take. This is a story about a jazz musician who chooses to side-step reality (which is harsh in its racism, its lack of opportunities, it's failure to offer viable modes of identity) and does so by taking drugs. He is loved. He is talented. But he is running away.
"Soldier's Home" by Ernest Hemingway might work also. The story is about a young soldier named Krebs who returns to his hometown (a week after all the other soldiers) without any kind of welcoming. He tries half-heartedly to fit back into society. Another story of, as stated above, "the American dream gone wrong."
Upon reading your question, the short story that popped into my mind immediately was "Winter Dreams," by F. Scott Fitzgerald. (Ironically, any of Fitzgerald's works would do. He always seems to write about the American Dream, . . . or perhaps more appropriately, the American Dream gone wrong.) An interesting comparison might be the idea of The American Dream of the Twenties: Achieved ("Winter Dreams") vs. The American Dream of the Twenties: Unachieved (Death of a Salesman). Ironically (or perhaps not so ironically?), both end with the same realization: hollowness and shallowness.
Now to explain a little bit more about "Winter Dreams," so that you can decide if you would like to use it for your classroom comparison. This short story, of course set in the 1920s just like Death of a Saleman, is about a simple golf caddy named Dexter. Quite simply, his golf experience puts him in touch with a beautiful and rich female golfer named Judy Jones. Dexter falls for her, . . . but she is unattainable until Dexter gains both wealth and power. (Thus another question arises, are wealth and power the true American Dream? Or is it something else?) Dexter does achieve such in the context of the story; however, although he succeeds in attaining Judy for a month or so, he eventually loses her and, even worse, Dexter eventually finds that Judy's reality couldn't live up to his dreams about her. Dexter finally admits that his "dream was gone," and ponders the hollowness of the universe.
My particular mention is not a short story, but a play by David Mamet. "Glengarry Glen Ross" is a rather brutal modern analysis of the salesman life. Like Miller's work, Mamet's offering helps to dissect the life of those committed to "the deal." The idea of "Always Be Closing" is how business is not only transacted, but how life is to be lived. The play exposes how the pursuit of success comes at tremendous moral and spiritual costs. The trappings of wealth cannot mask the corroded center of those committed to nothing short of material glory. This is similar to Miller exploring the hollow nature of an American Dream constructed in singularity, as opposed to multiplicity.