In a short sale situation, you do not owe the difference to the bank in all cases. In a non-recourse state, the short sale generally ends the seller's commitment to the bank. In a recourse state, the bank *may* forgive the deficiency, or they may retain the right to go after you in the future for it. From your username, I presume you are in DC, which is non-recourse. You should consult with an attorney and a real estate broker to determine the best course of action.
The first step would be to get the bank to agree to a short sale in the first place, which would be your first opportunity to try to get their agreement to forgive any deficiency. On an amount this small, it's possible, even though it represents a fair percentage of the amount owed. Short sales take a very long time, and the final amount/seller/contract/etc. are also subject to bank approval, and would be another opportunity to get the bank to sign off on forgiveness of a deficiency. Your attorney and/or broker will be the ones best equipped to help you get concessions from the bank.
If they do retain the right to get you to pay the deficiency, it is likely that you would at least be able to work out a payment arrangement with them.