In a way, the theme of the American Dream does surface in "The Chrysanthemums." Elisa has visions of a more exciting life, a more exciting American Dream.
Elisa has a comfortable but limited life. When she encounters "the man", she and he connect by talking about the chrysanthemums. As she warms up to the man, she notes that it must be nice to be able to travel as he does. The man replies that it is no life for a woman. But through their connection (via the flowers), she feels like she has made a connection, not just to the man, but to the man's lifestyle. It has opened her eyes a bit and she begins to consider other ways of getting out of the confines of her limited life. She believes she has gained strength from this encounter. With her new attitude as a strong woman and her old way of being accommodating and meek, she shifts back and forth between her new and old roles:
For a second she lost her rigidity. "Henry! Don't talk like that. You didn't know what you said." She grew complete again. "I'm strong," she boasted. "I never knew before how strong."
Here, she indicates that she has a kind of awakening; that she is strong enough to change her attitudes about what a woman's life is, or could be.
Elisa is contending with society's expectations of gender roles. For her, the possibilities of becoming something more (a general definition of the American Dream) have to do with breaking through those boundaries and expectations. In the end, seeing that she was betrayed by the man who indirectly opened her mind to those possibilities, she retreats to her expected role, and cries "like an old woman."