What percent of the population works for the government?

There was a high water mark in 1954, where the Federal Government accounted for a little over 5% of the entire workforce. Since then, that percentage has gone down, more or less, to a little under 2%. Under Obama, the government has shrunk to its lowest level in the history of the country to this level. Whether he can take credit for that or whether that was an irresistible historical force is up for debate.

But if you mean "government" as in all levels of government, which includes state and local, I believe this number is around 18 - 20% of the total workforce. Local government personnel has skyrocketed in recent years.

Not a large percentage. I estimate about 20 million.

if you include all people who depend on the government for income including welfare, teachers, police, military, politicians and government contracts it is now just over 53%