Yes, the United States Government is functioning as a government as it is successfully governing the people. It may not always govern for the will of the people, but it maintains important infrastructures that make modern life possible. Thus, it is very much functioning as a government. Whether or not it is functioning correctly is another story.
(I don't mean to offend anyone or say that this government is a horrible thing. I simply think that there are ways this government of the people, by the people, for the people could be improved)
The United States as a form of democracy utilizing the "First Past the Post" system and gerrymandering results in a government which would ultimately yield a relatively moderate two party system.
Additionally, the United States Government doesn't function according to the will of the people. The United States Government as a representative government means that the representatives in it's political office represent the people but function based on their own beliefs and opinions.
Thirdly, I would like to point out that the average lay person has no direct impact on who the president is. That Privilege falls to the Electoral College, under the 23rd amendment of the constitution. (More information on that here: http://www.Archives.Gov/federal-register/electoral-college/about.Html )
Ultimately, this government of the people, by the people, for the people, fails to truly recognize the power and worth of those on the outskirts of society, those who can't fend for themselves, those who don't conform to the status quo, those who are not well off or better, and those who "fail to contribute" to society.
Let me leave by asking you this: If the government is truly fair, why do you needs millions of dollars to even have a chance of becoming the (kind of) democratically elected leader of this great nation.