If your mortgage company gets an escrow from you each month in payments, they will pay the property taxes. If you do not pay the taxes, several things. Depending on your lender note (mortgage agreement), the lender may be able call your note in full, as a result of breach of contract. If you can not pay it, they can foreclose.
Prior to that, the county will assess fines and penalties for non payment. Eventually, they can sell the home for taxes due. That takes a while, but in that case, then you are still on the hook to the mortgage company for the loan - even without the house.
I would not recommend waiting around to see which is the worst of all. If you are having trouble making the lump payment, I would call the county, maybe there is a payment plan. Or, talk to your mortgage company and see what you can do. If you have equity in the home, perhaps you can take a equity loan out or refinance so your payments include the taxes.