Most poor people have productive jobs -- often multiple jobs -- and they are working longer and longer hours but remain mired in poverty. This is not caused by lack of opportunity alone, it's also caused by lack of power to change the systems that create and continually recreate poverty.
Many people equate the American Dream with the attainment of a set of possessions -- a car and a home or a rising standard of living. Those are certainly desirable, but the more important element differentiating the U.S. economy from most others is social mobility.
A homogenous and self-perpetuating elite is a bad thing for any society, and particularly for the United States. Alone among nations the U.S. envisions itself as the place where citizens can and should rise as far as their combination of talents and hard work can take them.