Currently, states with conservative governors and conservative legislatures have already fixed their own budget problems. Utah, for example, is doing great. California, on the other hand, insists on demanding expansive social services that they can't afford. When you spend more on social services than you bring in from taxes, your budget will be out of balance. Liberal state governments are not willing to accept measures to correct their budget problems because it does not benefit them politically to do so. They are unwilling to do the right thing but they can.
What it takes is simply to make smart decisions with their spending, not spending it recklessly or wastefully on things that don't matter or are too expensive to afford. Further if they stopped embezzling the money they do get and put it towards things that needed it or towards the debt itself even, that would also help to stem the tide. So yes, the states can fix the budget problems if they learned to be prudent and quit stealing for their own gains.
Yes states can fix there budget problems if they can organize every single penny of where there money goes even if they have to make cuts here and there. If they make sure that there is no fraud happening and that everyone they give money is using it the way they should be using it. And it does not go anywhere were it is not needed immediately.
States that are currently facing serious budget problems can manage to pull themselves out of their financial holes with strong leadership and sound decision making. If state leaders exercise stout fiscal responsibility and devise creative ways to encourage business growth and generate revenue, states can continue to bounce back from the struggles they now face as the economy continues to improve.