In general your tax payment is much lower than your house payment, and so if you can pay the house off, you will have or should have no problem paying the taxes. Watch the local politics because everyone saw this does fail but it is pretty rare overall. Meanwhile people do lose their job and the payment portion of the house is a lot of money and so you can lose your job just because bad luck and in turn you lost your house.

Or to put it a different way, if my house was paid for, it would hurt, but I could make all ends meet just working fast food jobs. It wouldn't be an easy life, I'd end up walking a few miles to the nearest fast food place because I couldn't afford a car, but I could at least keep my house.