I think that this argument is particularly weak when compared to how government actually performs. However, politicians are not motivated solely by the public's best interest. Generally, they are motivated by the desire to be re-elected. I will admit that the strength of a democracy is that it tends to align a politician's self-interest with those of the public's. However, this is not always the case and to pretend that it is is particularly naive.
However, what if we assumed that politicians are only motivated to do what is in the public's best interest. Given this, there is still the problem of determining what the best interest of the public is. Some people want a single-payer health care system, others do not. Some people want to ban abortions, others do not. How does any one know, even politicians, know what is in the publics best interest? I contend that even if we given politicians the benefit of the doubt on what motivates them, they are still unable to determine exactly what is in the best interest of the public, or more generally, what the public wants.
What I find particularly interesting about the people who make the claims that state that government is run by the general population, is that in the next sentence they usually claim that the reason the government is not doing what they think is best is due to special interest's influencing politicians! How can it be the case that the government is run by the people, but also run by special interests? For example, the quote from the individual in the Missoulian was from someone who was protesting Representative Rehberg's stance on health care reform. At this protest, people were claiming that the congressman was not doing what the majority of people in Montana want. This seems to be a clear contradiction in their thinking. Is government "of the people," or do politicians simply do what they think would make them better off? I believe that the latter is the answer, and that is partially why I am skeptical of the government's involvement in any sector of this countries economy, and people's lives.