Yes. If the value of your home drops, making the amount of your mortgage higher than the actual value of the property, you are considered to have an “upside down mortgage.” However, an upside down mortgage is just like any mortgage: it is a contract that legally binds you to fulfill your obligation of paying the loan in full. The decline of the value of your home does not release you from the responsibility to pay the loan. Moreover, if you sell the house, and the sale proceeds are not enough to fully pay the mortgage, you will be liable for any remaining balance.
While you are still personally liable for your mortgage even if your house is worth less than your total loan amount, your lender may have a loan modification program that might help lower your monthly payments. Contact your lender to see if it offers any such programs. If your situation has deteriorated, and you face foreclosure, you may want to contact an attorney to discuss your situation and any remedies available to you.