No, The taxes will become a lien and paid when the short sale closes. You are not personally liable for the taxes.
Any individual seeking legal advice for their own situation should retain their own legal counsel as this response provides information that is general in nature and not specific to any person's unique situation. Circular 230 Disclaimer - Advice given in this response cannot be used to eliminate penalties with the IRS or any other governmental agency.
Do not pay the property taxes, they will be paid through escrow.
I guess I wouldn’t feel lawyerly unless I wrote a disclaimer to this answer – after all, that’s what we lawyers are trained to do. So here it is. Disclaimer: Trying to provide a complete answer to a brief question without meeting the questioner and without getting all the facts is much like internet dating. Despite what you have been told by the person you’ve met online (and don’t they always put everything in the best light for themselves), once you meet them face to face you realize how much has been left out. People tend to bend the facts and there is always the other side to the story. So, this answer is about as valuable as the price that was paid for it. It should not be considered legal advice. It is meant as a general overview of how the law could apply to a very broad set of facts that may not have any applicability to the actual circumstances of the person making the question. It is hoped to provide some understanding of the broad field of law that could come into play. No attorney-client relationship has been formed with the questioner and no attorney client relationship was ever anticipated by my response to this question. I would also like to remind you that I am only licensed in the State of California, and the answer provided is based upon my knowledge of California law.