Your comment that Loman's view of the American Dream is 'twisted' itself opens up many issues, socially, and personally. Willy Loman, in my opinion, represents the downfall of the american dream as it is traditionally viewed.
He does not represent an altered view of some beautiful fantasy. The american dream is essentially a flawed concept, and Loman shows this in devastating fashion. He buys into the commercialism of society (buying appliances he cannot afford), only to find that when items are paid off, they no longer work.
Loman does not see any error in his ways, fails to understand his crippling money problems, and when, in short monologues he admits defeat, he falls into a fantasy of the past. The past not being better, but being further from the desperate truth that he has no money, no prospects, and that the shining light of his son has fallen into the same fate.
The defining characteristic of the american dream through Lomans' eyes comes in his disregard for manual labour and work. Loman, clearly a talented craftsman, refuses to believe this to be a suitable profession, instead sticking to marketing and sales, and true entrepreneurial industries that cripple Willy Loman in the play, and many delusional people in real society (the true lo man, that Miller expresses).