You can sue the mortgage company but you will not win. The mortgage company is not obligated to accept a short sale offer. It is a business decision that they make on whether they will lose more money on a short sale or a foreclosure. Your best bet is to hire an attorney to fight the foreclosure action and possibly work out a settlement such as a forebearance agreement to buy you some time.
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Your best chance of sucessfully fighting a foreclosure is to serve a written Answer. When they serve you with the Summons and Complaint you have 20 days to respond in writing admitting or denying the allegations in their complaint. Serving a written Answer will prevent you from being in "default", which means they can proceed to get a court order to foreclose without further contacting you. You don't say when you were served or if you served an Answer. If you did serve an Answer, they are obligated to attend a settlement conference, which is another opportunity to see if something can be worked out with the court looking over their shoulder. Since there's no equity in the house anyway and neither one of you can afford to live there, you can also choose to just walk away from it. Most banks do not pursue deficiency judgments after foreclosure. It will hurt your credit for a while, but if you have other substantial debt, a Chapter 7 bankrupty would clear up all your debt, the foreclosure would be stayed until you are discharged, and in the meantime you live rent/mortgage free. Are you divorced already, or is that still pending?