The American Dream is a construct, often considered also as a philosophy of life, in which the individual hopes that hard work will be rewarded with a good lifestyle, and that every effort to build a high quality of life will bring on positive results. However, each individual has his or her own view of the American Dream. As a construct, people create their own vision of what the dream means to them. Hence, Willy's dream and someone else's dream will not be the same.
The problem with Willy's life, as a whole, is that he models it around the life of a successful man named Dave Singleman, a well-known salesman who supposedly made millions "out of his hotel room". Willy remembers the great amount of people attending Singleman's funeral. This is when he concludes that, being like Singleman, is the true key to success. Willy's dream does not involve personal sacrifice and hard work as much as it involves being "cool" and well-known. This is because, like Biff admits at the end of the play, Willy's dreams are "all wrong". They are wrong because they are not really Willy's own, inherent dreams.
Once the life and times of Dave Singleman become Willy's personal epiphany, he loses touch with all the things that truly matter: He does not nurture his kids, instead, he spoils them. He does not honor his wife. Instead, he has affairs to make himself feel "in charge". He does not even focus on his career. Instead, he places a lot of emphasis in what his career looks like in the eyes of others.
All this contributes to his ultimate failure: He has nothing to provide in the very end. As a result, he feels that the only way to leave something worth its value, is to kill himself and leave his life insurance to his two sons. Maybe they will have a better chance to reach their own American dream.
Conclusively, the American Dream negatively affects Willy Loman in that Willy's own construct of his dream has no real foundation. Willy should have not based his dreams on the successes of another man. No individual should model his or her life based on the life of another person. We each have a unique gift to give and Willy underestimated his own value as an individual. He made the ultimate mistake in trying to succeed in an instant: He tried to replicate Dave Singleman's formula for success. As we know, all came to nothing in the very end. It is just not the way the American Dream works.