They consider your ability to pay (income, debt-to-income ratio, savings), the value of the home, what they think they could get for it in foreclosure, loan-to-value ratio, and a whole host of other factors. It can't hurt to try to sell the property for whatever price you can get... the worst that can happen is you go through a bit of hassle and the bank won't agree to it.
This is not legal advice and is not intended to create an attorney-client relationship. The post is only an opinion. You should speak to an attorney for further information. The poster is licensed only in CT & NY. You can reach us at www.hamadlawfirm.com. If this post is useful to you, please remember to upvote it.
I think that its only a matter of time before you are in default on your mortgage. Whether by choice or circumstrances, you are not going to stay current on this mortgage.
That being said, there are few options. Short sale is one, deed in lieu is another, and foreclosure is the final solution. Most lenders will take the same applicaiton from you for consideration of both short sale and deed in lieu. Your lender will tell you the requirements. Many require the home to be listed for sale for 90 days. Usually the mortgage is in default when the short sale and deed in lieu are requested.
This answer is not specific legal advise. No attorney client relationship has been established. It is general commentary on the question presented, without the benefit of a full disclosure of all relevant facts. Seek an in-person consultation with a licensed professional.