A government has to at least be legitimate in the eyes of the majority. That doesn't mean it has to carry out every action that the mode wants... but it's manner of making decisions must meet the approval of not only a majority... but a large majority of the population.
If it fails to do this, it fails to be legitimate and it will not function without resorting to totalitarianism (which, I suppose in some loose sense can still carry out the purpose... for practical reasons, fear can equal legitimacy- I don't think it's sustainable and it certainly isn't any system I want to live under).

That is why populist movements tend to grow strongest not just due to widespread relative poverty, but due to the sense that powerful elite interests have taken legitimacy out of government.
The movements that status quo kiss-ups dismiss as the neediness of the poor are actually a response to the loss in faith in government due to the power of certain interests believed to hold more clout than theirs.
Are they mutually exclusive? No.
Are the fears of elite rule always true? Not necessarily.
But the fact remains that government has to remain legitimate in the eyes of the masses or it will fall. So in that sense, the government certainly must carry out the will of the majority.

__________________
"Man lives in the sunlit world of that which he believes to be reality. But unseen by most is an underworld, a place that is just as real... but not as brightly lit... A DARK SIDE!"
-opening from Tales From the Darkside