The Federal Government is able to just borrow to meets its needs but the states and local governments normally try to have a balanced budget. Either spending has to be reduced or some new forms of income have to be generated. Different states have done different things such as increasing fees for services or raising select taxes. Public transportation which relies on fares and subsidies is also able to raise their charges but in a great deal of cases this is just putting band aids on the problem.
The problems are highlighted by events like Chicago shutting its "non-essential" services for one day to save on payroll. In California which next to the Federal Government is running huge deficits Governor Schwarzenegger and the legislature balanced the budget through huge cuts.
The problem facing all levels of government is that in the last twenty years their spending has increased dramatically. They all signed contracts with their unionized workers providing health and pension benefits that at the time seemed affordable. Many of these assumed that the market would provided steady high returns and that tax revenue would keep increasing every year. Some states like New York signed new contracts in 2007 and 2008 that locked them in for ten years. Now that these costs are driving deficits it is proving hard to get the unions to renegotiate them. This means that either new money is found or eventually there will be layoffs or furloughs like in Chicago.
In California the state is facing lawsuits from all sorts of groups trying to prevent the cuts in the budget. These suits are forcing funding to be added back in and causing more debt problems. It also makes it hard for any proper budget to be developed. The money to pay for something a judge directs may have to be cut from another program that the legislature as is their right felt deserved more funding.
The problems of 2009 are only going to be worse in 2010. Many states used local governments used the "stimulus" funds to pay for salaries and medical programs. The stimulus funds won't be there next year unless Congress passes a second bill. This would add even more to the skyrocketing U.S. debt and may not be possible. The spending on this ended up not really being stimulative either unless you count as saving the jobs as helping the economy. This means that with another bad year of tax revenue and without Federal dollars propping up the budget cuts will have to be even harsher.
This reduced ability to spend on goods and services will continue to have a negative effect on the economy. Government spending especially in certain areas that are wholly funded by them -- like defense -- provides jobs and economic activity for many parts of the United States. If the money is not available next year then that activity will decline further continuing the recession.
The situation may require a complete rethinking of what government buys and funds. There is only so much it can do with the available funding. So far over the last two years there have only been minor attempts to restructure spending using tax and fee increases to patch the holes. Of course as California shows there are too many constituencies when it comes to spending. Unions will sue to keep their contracts in place. Interest groups will too to protect the spending on their issues, and so on.