Both Williams and Miller criticize The American Dream in their respective works. That dream is the spiritual one enshrined in the U.S. Constitution, "the pursuit of happiness," the Belle Reve alluded to in A Streetcar Named Desire; in Death of a Salesman, it is self-fulfillment. Peter Cash writes,
Ironically, this search for spiritual fulfillment quickly and easily becomes compromised and confused with the hell-bent pursuit of material success/affluence which in turn brings only spiritual emptiness.
Thus, as Fitzgerald demonstrated in his work, The Great Gatsby, it is the corruption of this American Dream into the amassing of material possessions that destroys. For, both Blanche duBois and Willy Loman tragically seek their happiness in three-dimensional form. Their searches lead only to a crisis of interpersonal relationships and of self-identity. In a sense, then, both protagonists of the two plays ride "Streetcar[s] named Desire" although this desire configures differently.
Search for Self-Identity
In Streetcar, one of Stanley’s dramatic functions is to be the antithesis of the Old South's sensibility embodied in Blanche's persona: that is, he is the foe of her aristocratic sensibilities behind which she hides her insecurity and need for identity. The animalistic Stanley senses Blanche's "pheromones" and immediately identifies her as a woman who enjoys physical relationships. But, what he does not understand is that Blanche uses sexual contact with men as a means of self-identification:
People don’t see you – men don’t – don’t even admit your existence unless they are making love to you. And you’ve got to have your existence admitted by someone.
Willy Loman, too, seeks his identity in objectification of his desires. "The Woman" supports his ego by saying she has chosen him over others because he makes her laugh and feel good. So, Willy, like Blanche, derives psychological comfort in this personal approval. But, he, too, ends in a crisis of identity because of seeking it in material objects.
Living in the Past
Both Blanche and Willy seek solutions to their failures in the past. Blanche flees her problems, seeking help in "the kindness of strangers," rather than admitting her failures; similarly, Willy examines and re-examines the past through memory as he tries to analyze what he has done wrong. Like Blanche, he lives too much in the past.
.... And always to have to get ahead of the next fella. And still — that's how you build a future.
He asks Ben how he made a fortune in diamonds in Africa. Also, he clings to the idea of "being liked and you will never want." But, this quest for personal approval fails both Willy and Blanche because happiness comes from one's own self-satisfaction and acceptance.
Denial of Reality
The protagonists of both dramas ride "streetcars" of desire and illusion that arrive at the metaphoric "Elysian Fields." Blanche attempts to deceive by hiding the reality of age and personal failures in marriage and career. Her placing of self-identity and spiritual happiness in the hands of strangers rather than within herself leads to her rape by the predatory Stanley and mental breakdown. Willy's delusion that the key to success is to possess "a smile and a shoeshine" leads to his failure. His superficiality in not recognizing the value of honesty and hard work added to his desire for material possessions as measures of success lead to his debt and failure to realize that happiness is spiritual, not financial or material.
Additional source: http://www2.le.ac.uk/offices/english-association/publications/bookmarks/70