When a government has 300 million+ people to represent, it needs to have very limited responsibilities and powers, because the common interests of so many people are very limited.
That is (cargo culting political attitudes aside) largely why the American relationship with the federal government is "adversarial"- the larger it grows, the easier it is for special, non-representative interests to take advantage of.
There's a similar story played out among union participation here; the larger the union, the less individuals feel that it is working exclusively in their best interests. Likewise: approval for individual congressional representatives is typically high, but Congress itself invariably has very low approval ratings.
I'm not sure I agree with that. The common interests of people are basically the same - education, health, housing ...
There are over 80 million people in Germany. Not in the same league as the US, but still a huge country. And I don't think (obviously this is not data) that people here feel the government don't work for their interests. In a very small country like Ireland (where I'm actually from) the government seem to me to be much less 'representative' of the people, due to cronyism and corruption (see current Irish gov scandal expected to bring down the government within weeks - http://www.irishtimes.com/opinion/fintan-o-toole-the-maurice...)
http://www.cnn.com/2012/03/09/opinion/flynn-expand-congress/