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.