Alaska would definitely take a hit if they left, but as Alaskan Survivalist said, I think we'll make it through.
Besides, there's still so much money on the slope, and the potential lack of off-shore development soon should keep us in business for a while. Most likely we'd lose a lot of slope workers, but there's still quite a bit of money from tourism, military funding, fishing, etc. to keep people going.
Sure, the State itself would lose a LOT of money, but they've been working on a bloated budget for a while now.
On the bright side, I might finally be able to afford that 40 acres (assuming I get all my finances in order before a bust)

Alaskans are a tough breed. I think we'll fare ok, but it may be a bit tough for a while. Until they find some other resource that they want up here again, and it'll be a boom-State all over again.