According to a study released by the Heritage Foundation 52% of all labor union members worked for the government (http://tinyurl.com/ygunb4g). To get an idea of how much this has changed over the past several decades, in 1973 only 17% of union membership was employed in the public sector (of course the other 83% were employed in the private sector).
Another interesting statistic is that the portion of American workforce belonging to unions has dropped from 23% in 1980 to 12.3% in 2009. Looking into that statisic more deeply reveals that in 2009 the percentage of private sector employees in the union was at 7.2%, while the union percentage of government workers in 2009 was 37.4%.
As government at all levels is forced to cut spending to reduce budget deficits, look for plenty of conflict with the unions representing public sector employees. The unions have already worked hard to oppose legislation for spending cuts in many states including California and Illinois (two states in real fiscal trouble). Also, look for the unions to continue their heavy contributions to influence political decision making at every level.
