I'm not expecting 100% energy independence on oil, just a reduction from our current reliance. It would be good for not just the local economy. Think about the entire process from exploration to that cashier at the gas station. It may only be a relatively small initial economic impact but it would still directly affect millions of people in some way. If a local economy improves it encourages growth. People move to the area, more businesses pop up, houses are built, the area grows. That local growth will have an affect on the state economy and although smaller, on the national economy also.
Right now the economy sucks and people don't have much money. If we force alternative energy and fuel which is more expensive it's just going to make things worse for everyone. If we do what we can right now to give any kind of help to the economy, once it improves we can more easily move to the alternatives because people will be more willing and able to afford the initial additional cost during the transition.
I'd even go so far as to suggest a temporary drastic reduction on some of the more restrictive and costly regulations for energy companies. Maybe combine that with an agreement that a specific portion of profits will be put toward the actual implementation of alternative fuel and energy production. Create an energy boom in order to help smooth out the path to alternatives.