Meanwhile, the Ounce of Prevention Fund says the budget would "decimate" programs for children. The group warns it could slash mental health services, child care, mental health programs and more.
Both groups urge state officials to go back to work and come up with new money for government services.
Lawmakers approved a budget over the weekend that falls about $7 billion short of covering expenses after they failed to agree on tax increases or spending cuts.
The governor and legislative leaders have begun negotiations on a new budget.
"I think the feeling in the room is very positive. That we are a team," said Governor Pat Quinn, (D) Illinois.
"We are meeting, we are talking," said State Sen. Christine Radogno, Senate Minority Leader.
"I'm very proud of the fact that we had a very successful session by cooperating with the Republicans," said State Sen. John Cullerton, Senate president.
But there was no cooperation in the House Sunday where more than two dozen Democrats joined all the Republicans who voted "no" on the proposed 50 percent increase in the state income tax. State Rep. Tom Cross, House Minority Leader, indicated if the Democrats made some changes in union contracts, pension rules and other reforms, there might be some yes votes the next time the tax bill comes up:
"We made some observations of things we thought we need to see proceed over the next few weeks and months on reform that we've talked about before," said Cross.
That left longtime House Speaker Mike Madigan to explain why he couldn't get more of his members to support the tax increase.
"It's very understandable that there were certain Democrats in the House who were very concerned about the impact on the general population of the tax increase," said Madigan.
The governor said while the negotiations preparing for another tax increase vote continue, programs for children, the elderly and disabled will be notified of impending 50 percent funding cuts.
"You have to send the notices out to let people know what the possible consequences are," said Gov. Quinn.
Finally, Speaker Madigan assured he would never play politics with the budget and his daughter, Attorney General Lisa's, reported ambition to run for Quinn's job.
"There's a whole body of people in Illinois who want to criticize me all the time. Lisa Madigan is going to do what she wants to do and she'll do it on her own," said State Rep. Madigan.
The governor has said he won't sign the $26 billion capital construction bill until the lawmakers agree on new revenues to save social services programs. But the clock is running; the budget cuts become effective on July 1.
The Associated Press contributed to this report.