There are some key factors that aren't always focused on:
1. People in government don't want to cut things that give them power (or at least job security). And in a bureaucracy that usually has to do with how many people report to them. No one wants staff cuts. They will try to cut services, if they have to cut something. I.e., keep their people, even if the people do less.
2. Like Joe pointed out, government threatens to cut what people value (e.g., kids education, police and fire protection). The threats are an attempt to continue doing what they are doing, or to twist arms to increase taxes.
3. With school funding, which as Dean mentioned is a major portion of local taxes, the tendency will be to do thing like cut the number of days they will keep school open, or cut night classes, or community services, and cut the supplies, and cut classes that have higher costs (like art, music, etc.), but they won't want to cut the number of teachers, clerical staff, administrators, or anyone's salary.
4. They will also look for non-cuts, or ways to move things "off budget" or to borrow from rainy day funds, or any other way to kick the can down the road, or to find new kinds of taxes.
In Wyoming, as an example, the teachers union has a lot of sway with the state legislators despite the fact that Wyoming is NOT a strong union state. But that teacher's union (and a state Supreme Court ruling requiring equal facilities across counties) was able to get the state to force localities to engage in a massive increase in new school buildings. Of course with more classes, they now need more teachers (Surprise!). And as Wyoming's ability to fund government from the declining mineral severance taxes declines they will be looking at those 4 factors I laid out above.
Long-term there is no hope for real success without most people understanding that government should only do police, military, and civil courts. Education, charity, and all the other things now being done by government have to be taken care of by the private economy.