Studies [1] on this question show exactly the opposite. The view of the majority of the population shows no meaningful impact on the policies that our government actually chooses to adopt. The interests of "economic elites" (to use the phrasing of the paper) do tend to be predictive of what passes. Their 'disinterests' tend to be very strongly predictive of what does not pass. The study concludes that the US has already devolved into an oligarchy though "Americans [still] enjoy many features central to democratic governance, such as regular elections, freedom of speech and association, and a widespread (if still contested) franchise."
On the other hand, I am always reluctant to link to social papers since data can be so easily massaged to affirm nearly any presupposed conclusion. Do you have any evidence or logic to support your view that the masses have any substantive and, more importantly, lasting effect on policy? I do not think it's self evident that the masses are having any direct effect on the current themes of net neutrality and PIPA/SOPA/CISPA/CISA. The apparent effect seems more due to the fact that very influential "economic elites" are themselves divided on the issues.
[1] - http://www.princeton.edu/~mgilens/Gilens%20homepage%20materi...