CHICAGO — Cook County, Ill., faces a nearly 16% shortfall in its general fund next year as revenues continue to fall, officials said yesterday as they unveiled preliminary 2012 budget numbers.

The county’s deficit could reach $315 million in 2012, out of a proposed $2 billion general fund budget, said county board president Toni Preckwinkle. The preliminary all-funds budget totals $3.2 billion.

Finance officials said they expect to see a $116 million shortfall in the current year.

About $96 million of this year’s shortfall stems from a deficit in revenues from the county’s massive health system. Moody’s Investors Service in mid-June downgraded the county to Aa3 from Aa2, in part due to challenges facing the health system, which accounts for about a third of the county’s total budget and is chronically riddled with deficits.

Fitch Ratings and Standard & Poor’s both rate the county AA with stable outlooks.

The county is relying on $92 million in savings from a debt refinancing that pushes to the future debt service payments due in 2012. The current budget relies on pushing off $85 million in payments. The county is expected to enter the market in the next two months to achieve those savings.

Preckwinkle unveiled the budget figures Thursday, saying she would call for 5% across-the-board non-personnel cuts and warning that layoffs were “inevitable.”

Cook County last February passed a $3.1 billion budget that brought down a record $487 million deficit with a mix of cuts, one-time revenue measures, and the savings expected by the debt restructuring.

“We did a lot of the easy stuff in the last budget cycle,” Preckwinkle told reporters at a press conference Thursday. “It gets harder and harder to make the cuts you have to make. It will be hard to do the budget without layoffs, but the magnitude is the question.”

New estimates project that revenues in 2011 will total $2.2 billion, which is 5.2%, or $122 million, less than expected. Spending also is slightly down, by just under $6 million.

General fund revenues in 2012 are expected to total $2 billion, which is 14%, or $318 million, less than 2011.

In addition to slower-than-expected patient fee collections, the county faces declining revenues due to the planned roll-back of the final 0.25% of a deeply unpopular 1% sales tax increase implemented by the former administration, according to Preckwinkle. The county board has voted to roll back the tax hike in stages, with the final 0.25% repeal scheduled for next year.

It is the first time the county has released a preliminary budget and follows Preckwinkle’s new executive order that one be released by July 31 every year.

Preckwinkle won office in 2009 after beating Todd Stroger, who ran the board after his father, long-time president John Stroger, fell ill.

Preckwinkle campaigned on a platform of restoring fiscal responsibility and transparency to the county and the promise to roll back the sales tax increase.

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