The state and local government pensions I'm familiar with should actually be safer than most pension systems -- in theory, the government agency makes its required contributions to the trust fund at the time the employee is paid. The bigger state and local pension systems are some of the largest institutional investors, so their fates are more tied to the market than their member governments.
As with any other pension system, if a lot of the trust's holdings are in bonds, and those bonds end up in default, that would be a problem.
The government pensions schemes are facing the same problem as Social Security -- people living and collecting benefits longer, health care costs going up (for those that include long term health benefits), and so on.