According to the U.S. Bureau of Labor Statistics, government accounts for about 8% of jobs in the United States. Here's the breakdown using numbers easily accessible on the BLS website (all numbers from 2006 or 2007):

1,774,000 Federal government civilian employees, excluding Post Office
615,000 Post Office
1,172,913 Military enlisted
230,577 Military Officers
2,424,000 State government (excluding education and hospitals)
5,594,000 Local government (excluding education and hospitals)
That's a total of 11,810,490 government jobs.
The total number of jobs in the U.S. in 2006 was 150,600,000, so government employment makes up 7.84% of all jobs.
In 2007, the U.S. population (according to the Census Bureau) was 301,621,157, so about 4% of Americans are employed by the government.

According to a study by Paul C. Light, a government professor at New York University, the Federal Government also employed 14.6 million contractors in 2006. This was an increase of 2.5 million since 2002, and the study attributes the increase directly to contractors hired as part of the war on terror. (reported in the Washington Post)