There are a couple of reasons Willy's stake in his "New England-ness" are important to the American Dream. The first reason is the "up-by-your-bootstraps" mentality introduced by our Puritan forefathers to that region. Unlike other parts of the world, your place in life is not determined by your birth into a specific class. You can literally rise above it, at least socio-economically.
Along with this thinking is the belief that everyone has their part to do. Willy sees himself as doing a necessary job, performing a necessary service. Capitalism thrives on commerce. Willy sees his job as worthy too, which is part of the reason he becomes so depressed at his failure. He has worked hard all of his life and gotten little, if any respect, even within his own family. He expects, too, that one day he will be rewarded for his efforts. The money never materialized.
These beliefs (hard-work, individual effort and value, and eventual reward)are fundamental to the American psyche. Despite reports to the contrary, Americans are some of the hardest workers in the world. But like Willy, many live up to the ideals we have absorbed without the final rewards of money and respect. As Willy discovers, "the pursuit of happiness" doesn't always mean the *capture* of that elusive creature.