County Tax Liens against your property complicate the sale of your home. The real question is, has or when will the county take tiltle to the property. Once this occurs you lose any right or claim to the property, and the new owner (the county) may keep the property or dispose of it by sale. The tax liens will be the first to be paid in the proceeds of the sale and then the mortgage. The homeowner now former homeowner has certain rights on payment of the taxes (timelines). You should consider talking to a real estate attorney to find out exacly what your rights are.
The question then is how much is the home worth, how much do you owe. Are you in arrears in mortgage payments. If so how long? etc etc. Will there be any proceeds left when the home is sold? If the homeowner does not have enough in the proceeds and cannot close this results in a short sale. Someone has to come up with the difference. If you are short and obviously cannot pay then the buyer pays. This needs to be disclosed to any potential buyer during the listing.
So as you can tell there are many factors weighing into the process of selling your home. The answer to your question is if at the end of the sale and going to the closing table if everything breaks even it's a regular sale and the proceeds go to payment of taxes, mortgae, and any other lien holders. Permission may need to be granted from each lien holder in writing that a sale can go forward.
I strongly encourage you to contact an attorney right away, or pay the taxes.