Quinn spokeswoman Ashley Cross says they wanted AFSCME to reopen its contract to consider concessions, such as unpaid furlough days and a pay freeze.
AFSCME Executive Director Henry Bayer says the proposed concessions would cut workers' pay by up to 15 percent and would still result in 1,000 layoffs.
To help deal with a huge budget deficit, Quinn has proposed 2,600 layoffs, including many in Illinois' prisons.
"We're in dire straights," said Gov. Quinn
"It's not safe. We're burning out our members. It's costing us more...that we wouldn't have to pay if we'd just hire enough staff," said Aders Lindall, AFSCME.
Money to fund college scholarships is also being cut. But Quinn says he has no choice.
"These are not wasteful cuts, they're painful cuts," said State Sen. Kwame Raoul, (D) Chicago.
The cuts include
Governor Quinn said the legislature left it up to him to make the tough choices, while still refusing his call to increase the state's income tax.
"We have to deal with fiscal reality. That we have a revenue shortfall to pay our bills. We have a $3.9 billion shortfall we have to pay. We're a deadbeat state," said Gov. Quinn.
The Associated Press contributed to this report.