The Manhattan Institute for Policy Research has issued a brief policy paper on this issue. It points out that in 1955 almost no government employees were represented by unions, and that Federal employees still may not bargain collectively over salary and benefits.
The key benefit of this paper is its thorough discussion of the differences between public and private sector unions. Here is an example of those differences from the AFSCME Newsletter of September, 2006:
We elect our bosses, so we’ve got to elect politicians who support us and then hold them accountable on our issues.