The US system today most closely resembles a utilitarian system. Utilitarians believe that society should be ordered in such a way as to provide the greatest amount of good for the greatest number. Our society, with its emphasis on free markets, is set up in this way.
We tend to think that free markets will bring the greatest overall level of prosperity. We do not worry too much about the inequality that comes along with the free market. We feel that this inequality (even when it leads to some people living in true poverty) is an acceptable outcome given that the free market system can make life so good for the majority of us.
In this way, we adhere most closely to utilitarian ideas of justice in our system today.