The discussion has been good so far - but mostly tilted toward getting that debt down by any means necessary. That's important, but let me argue toward savings just a little bit, and its more than money...its forming habits.
I think its important to have a bit of savings (about a $1000) before you do the heavy duty pay-down-the-debt. Psychologically you need a cushion not only because things happen, but because its important when you are building good habits that you
avoid bad habits. Dipping into your debt to get by only reinforces a bad habit; dipping into your savings encourages you to save a little bit more because you're thinking "Whew! I'm glad I had this."
I think it is also important to save a little bit even while you are paying off the debt, but just a little. The worst case scenario is having $10,000 in savings and $10,000 in debt! Again its a case of habit. Fiscal responsibility is more than just getting your debt down, its what you do after you pay off your cards.

You need a good savings habit in place to pursue your goals; you get the habit by doing it and doing it through thick and thin.