Alvarez made her case against proposed 10 percent budget cuts at a hearing attended by County Board President Toni Preckwinkle.
Preckwinkle said balancing the budget will be a painful process with lots of departments making deep cuts. But Alvarez said those cuts should be different for each county agency and there should not be a cookie-cutter approach to making reductions.
"I told her that I would try to meet it, but I'm not optimistic and at this point I'm not there," said Alvarez.
Alvarez said she's tapped out, that the maximum she can reduce the budget for her department is 8 percent.
Preckwinkle has called for a 16 percent budget cut from nearly every department to plug a $487 million deficit this year.
After some debate, Preckwinkle and Alvarez agreed to 10 percent.
But Tuesday, before a county budget hearing, Alvarez said she is facing layoffs of 200 staff members, including dozens of prosecutors, which could affect criminal cases.
"There's a direct hit to public safety here," said Alvarez, "a direct hit to services that we provide each and every day."
Preckwinkle says there is a way Alvarez can avoid laying off prosecutors by focusing on trimming her administrative staff.
The board president says she plans to hold Alvarez to 10 percent.
"As I said from the very beginning, no one is absolved, no one is alone, and the one person who is making the least amount of cuts is reneging on the deal," said Preckwinkle.
Also making tough cuts is Cook County Sheriff Tom Dart, who found ways to trim 12 percent from his budget, including cutting the graffiti and K-9 units.
"That's the type of cost that has to be made when there is mandates and orders to cut the budget," said Jesus Garcia, Cook County Board.
"A lot of the amendments that will come will fundamentally change the way Cook County operates, and that will mean the future beyond that may be better years," said Peter Silvestri, Cook County Board.
Budget hearings will continue throughout the month.
The board has to approve the budget by February 28.