The new rule on whether you should pay off debt vs. building savings is that there are no rules. I know I've been following the rule of pay down debt before adding to savings and I've touted the benefits of this strategy: debt costs more long term, savings accumulate slower. But all bets are off in this economy.
Suzy Orman just released an update to her 2009 Action Plan, and I've got to agree with her on this. Suzy says, "If you do not have a stash of cash and you have been using all your extra money to pay down your credit card debt and they keep closing your cards down- what are you going to live on if you lose your job? Chances are you may not have any available credit limit to use to rely on since the cards are reducing those limits, you will not be able to get a new card since you are now not employed. So to help you in the event you lose your job my advice is to pay just the minimum required on your credit cards every month, and then use every extra penny you have to build your emergency savings fund."
Make your goal to have 8 months of living expenses in an emergency fund. As long as you continue to make minimum payments on your credit cards your credit score should be fine. That is unless the card company doesn't reduce your limit or close down your card, which they are less likely to do as long as you pay the minimum. But don't be tempted to use the cards for charges that are not emergencies. And only then if you don't have other funds to cover the event.
If you already have a substantial emergency fund in place, keep paying down that debt. These are unusual times and it's important to be prepared for the worst while remaining flexible to changing your strategies.