Cook County has had a 7% annual cap on assessed value increases since 2002. (Said cap is also undergoing a scheduled phase-out, which will increase tax bills more steeply than assumed here.) Property tax bills will rise this year, despite falling property values; this graph explains why property taxes will in fact take a while to catch up with market values.
‘A cap, which gives homeowners comfort in a rising market, can, however, create the opposite effect in a down market. In Texas, which sets a 10 percent limit, property values rose by as much as 18 percent per year during the past decade, but assessed valuation could go up by only 10 percent per year. As a consequence, a large gap exists between real market value and taxable value. Because of that gap, assessed value may go up this year even though market value is coming down. Until the two come together — the market value falls to the level of the taxable value — 5 to 10 percent increases in assessments are a real possibility. “That’s going to be another contributory factor in taxpayer frustration,” says [Guy] Griscom, who is the assistant chief appraiser for Harris County. “Legislatures didn’t look at that side of it when they gave property owners the benefit of these caps. Ultimately you have to pay it back. This is not what people want to hear.” ‘ – Penelope Lemov, Governing magazine
(Assumed $100K property in year 2002 [and that assessed value equaled market value, which is probably not the case in Cook County], using 2002-2009 price appreciation trendline reported for zip code 60647 at Zillow.com, then assuming a 30% drop from 2008 peak by 2010.)
west north 
OK, so you take the hit later, right?
Perhaps folks are caught off guard, but a deferred payment still sounds better to me.
Pretty much. Still, a lot of people are going to be confused by rising tax bills in an era of sharply falling property values. (In some places, like downtown, it looks like 2003 prices all over again.)