Speaking directly to a mortgage professional is the best way to have your questions anwered regarding mortgage. There may be a way around this in that you can sell your property, pay your debts and then close on your new property, with paying off the debt as a condition of close. Unfortunately, you do not mention your credit; if your credit is not effected by the debt, then you could be fine, but it takes longer to repair credit.
Again, contact a mortgage professional. They know the ins and outs of the current laws and you are under no obligation to use them, even if you receive information from them. In otherwords, do not be afraid to call as an inquiry.