I think that the proliferation of accessible media is responsible for the growth of the public sector. The 24 hour news media and accessible internet and social networking tools like Facebook and Twitter make it possible for people to learn more about what is going on around them, but also to make their voices heard. People voice their opinion about everything freely and constantly. They do so collectively and their voices get heard.
We added a gigantic new entity into the federal government: The Department of Homeland Security. It's massive, with about 30,000 employees. We are also involved in two wars, and the number of elderly people in this country is growing, as pohnpei suggests, so the entitlement programs that serve them are growing at the same rate.
In my opinion, the public sector has grown so much because people want more and more things from the government. In addition, the interests that are helped by each particular government program want to keep those programs alive and other people lack any serious incentive to kill any programs.
As an example of the first factor, people (especially the elderly) were very much in favor of the Medicare drug benefit. They supported Pres. Bush in passing this and that expanded the private sector.
As an example of the second, farmers tend to want to keep farm subsidies. No one else has much of an incentive to kill those subsidies because the benefit that any individual taxpayer got from killing those programs would be miniscule.