Though I do think there are plenty of reasons to connect Of Mice and Mento the notion of the American Dream, I don't automatically like to read this book as a comment on the impossibility of the American Dream.
Crooks, Candy and Curley's wife are the most thoroughly disenfranchised characters in the book. They have no power and there is little chance that they will ever be in a position to gain power over their own futures and their own lives in any sense that is meaningful. This state of being is directly connected to the economic power of each individual.
We can take this set of circumstances to mean that the Dream has failed these characters, but I read the book as suggesting an exclusion, not a failure. Even George is excluded from a real chance at independence (financial/economic self-determination), and this is despite the fact that he has some moral power in the society of the book.
Social mobility is not the monster. Believing in social mobility as a political virtue is not a vice. Rampant discrimination, scarcity of resources and a culture of fear and economic abuse - these are the monsters.