This is a very thorny issue, I am going through the same struggles with a fixer-upper property that is overassessed by at least 500,000.  I have also spent time dealing with county tax agencies.  Here are my thoughts, based on experience:

1: Taxes will not be reassessed lower unless you ask.  Most counties only have one window in which to appeal tax rates, and that is in the fall when assessment letters are mailed out.  Until that time, the increased tax must be paid.

2: Property taxes assessed by the county are not only subject to the valuation of your property by a county assessor, but also to a divisor based on the cost of providing services (and godawful public pensions) to the county workforce and related county projects.  If the county in which you are looking has not reduced their own expenses, dont expect a huge reduction in property tax.  Even with a reassessed value, an increased divisor will wipe out much of the savings.  Since the county's jobs and pensions are dependent on property tax assessments, it is probably safe to say that the county would rather see real estate prices fall, keep the divisor high, and rake in the same tax revenue that they had built up during the bubble. 

3: If you are looking at a fixer upper in a high-end neighborhood, dont expect any major tax changes since the overall assessed value will be based on comparable properties and sales in the area, and NOT on the interior condition of the residence in question!

4: Get a tax lawyer - a tax attorney with familiarity in your county can be your best asset, and could get the overall tax bill lowered more than yourself.  His/her fees will be more than offset by a year of tax savings.