The assessed value and the appraised value are two different things. The assessed value is what the town uses to determine your taxes. In "theory" it should represent the value of the home. It should never be used to determine market value. It's great to have a low assessed value as your taxes are lower.
I would venture to guess that most homes are over assessed currently. Market prices dropped faster than assessments. My assessment went down last year for my home. Not enough. I grieved my assessment and had it lowered an additional $110,000. This is going to reduce my taxes by thousands every year. This is something every homeowner should think about.
In your case, if the appraisesd value is less then you agreed to pay then renegotiate. If you haven't signed contracts you can renegotiate or walk away from the deal.