Was there a poverty trap in feudal Europe, or these American lands before the Americans? There's a poverty trap because the economic system needs a poverty trap to function. It is not due to neglect, but due to a massive amount of attention that poverty exists in the U.S. - it takes a lot of work and effort to keep people poor, in a country where GDP and productivity have been rising for a long time.
What would the reason for U.S. poverty? Well it could be the legacy of the New Deal and progressivism, although that would not explain massive poverty in slums and rural areas at the end of the 19th century in the U.S. It could be due to a liberal idea of a lack of caring - although the New Deal, the Great Society and so forth brought a lot of focus on these things.
Or poverty can exist because it is a necessity, a cornerstone of the economic system. The reserve army of labor ( http://en.wikipedia.org/wiki/Reserve_army_of_labour ) and all of that.