In Arthur Miller's Death of a Salesman and David Marnet's Glengarry Glenross we find very similar thematic elements that convey upon the reader the reason why both plays would challenge the topic of the American Dream.
This is evident in the very similar characters of Willy Loman and Shelly "The Machine" Levene. Both, older salesmen down in their luck, are desperate. However, as young, up and coming salesmen, they once taste the spills of glory when, at one point, they are both able to declare that they have achieved their own ideal of the American Dream.
To Willy Loman, the American Dream comes near 1928 when he owns his own home, is married, has two boys (one being a high school superstar, to boot), drives a red Chevy, and insists that he is well known and well-liked among his customers. These are Willy's claims to his achievement of "the dream". However, Willy suffers through the huge changes that take place in his city, complete with its lows in the economy. He no longer can call his home "his dream home", for now it is surrounded by brownstones. His Chevy breaks down. No sales come up. He loses his dream in the end and kills himself to get insurance money for his sons.
Similarly, Shelly Levene is so popular once that he is dubbed "The Machine" by his firm, Glengarry Glenross, for selling so well. Granted, Levene and his colleagues actually sell anything, from good properties, to worthless pieces of land on which very few people settle. Here we see that the "American Dream" of the Glengarry Glenross clients is similar to Willy's: they all want to "have", and to "own". Based on that version of the clientele's "American Dream", the Glengarry Glenross firm makes its profit.
Levene, back in his good old days, would have been able to sell that and more. Now, when the firm is going through enormous risks in sales to step up their game, Levene is falling so behind in his luck that he can't even afford gas. He is now a man who lives in a transient hotel, with a sick daughter, and no money to afford anything. He is so desperate that he ends up stealing leads from his own firm, and then goes to jail.
Hence, Willy and Shelly both lose their respective American Dreams once times begin to change, the economy becomes harsher, and enormous social changes bring utmost pressure. Both men represent the average American: the person who really does as much as possible to attain certain goods and services, but who ends up giving them up due to the change in the tides of a very unpredictable world.
Therefore, the challenge of the notion of the American Dream is that both plays claim that such a dream is not only hard to get, but also hard to keep. There is no way to assume that, once we have "made it" in life, we are safe from anything else happening to us.
The American Dream is an idea, and not a fact. It is a hope, not a mandate. It is something different to each of us but, most importantly, it is NOT a safe dream. It can be taken away from us by crime, it can be broken and ransacked by a bad economy, it can be killed by illness, or it can be simply impossible to get in some instances. Therefore, the plays show us to learn to stick to what we have and not let the notion of an American Dream lead us to greed and disillusion. We are not really the ones who are in control of the American Dream. If anything, with luck, the American Dream may ultimately pick us.