Joseph Duffy worries about what will happen when he dies and is no longer around to fight budget cuts that threaten services for his 29-year-old developmentally disabled daughter, Katie.

Despite her disabilities, Katie has a state-supported job at Cigna and has a weekly social outing. But nearly $40 million in proposed state budget cuts would threaten her delicate safety net, he said.

“She has a small world, but it is everything to her,” Duffy said. “If it is broken apart, it will destroy us.”

Duffy, of Wethersfield, was a speaker at a panel discussion Tuesday at the Capitol held to raise awareness of how $39.4 million in budget cuts would affect the lives of people with disabilities and their caretakers.

About 150 people, many developmentally disabled and wearing yellow T-shirts emblazoned with the words “Protect the Safety Net,” packed the meeting room to hear about the cuts.

Another parent, Carl Noll, 69, of Fairfield, said he also worries that his two developmentally disabled sons will be “out on the street” when he dies.

He questioned the priorities of a state considering more than $1.5 billion in new construction at the University of Connecticut while also planning to cut basic services for developmentally and intellectually disabled people.

“We’re perfectly willing to create a bond for the University of Connecticut, my alma mater, for $1.5 billion to support people on the other end of the scale, but we can’t provide beds for people like my son,” Noll said.

Several parents said the developmentally disabled feel segregated and discriminated against and urged the community to stand up against the cuts.

Another panelist, Patrick Johnson, talked about how a long history of chronic underfunding has affected his agency, Oak Hill, which provides services to developmentally and intellectually disabled people in 58 towns. His employees have not had any wage increases in five years. He said the agency needs a 4 percent increase next year and a 3 percent increase the following year just to meeting fixed costs.

Continued budget cuts would undermine progress the developmentally disabled have made in recent years, he said.

“What we are all witnessing right now is a march backwards and it’s really disturbing. We lose sleep over it,” Johnson said. “If this keeps up, over time our group homes will like mini-institutions.”

Johnson said nonprofit agencies have already made major cuts to their own budgets and are struggling to stay afloat. He said that 43 percent of Connecticut nonprofits had deficits in 2010 and that 72 percent would go out of business if they faced a financial reversal.

“They are right on the fringe of going over the financial cliff,” he said.

Most legislators seemed unaware of the panel discussion, but a few stopped in at the meeting at the last minute.

Senate minority leader John McKinney, R-Fairfield, was one such visitor. Invited to take the podium, he told the gathering that he believed the state should get out of the business of delivering social services.

“For 15 years I’ve seen the state compete against our private nonprofits. Every year I see the state continue to win and it’s not the right way to do business. The state of Connecticut should get out of delivering social services,” he said.

He said private nonprofits are more efficient than the state model.

“We spend a dollar every time you spend 50 cents,” McKinney said.

“Rather than cut the safety net, rather that cutting services, we can change the delivery model,” he said. “We can save $350 [million] to $500 million a year by the state getting out of the business, properly funding your organizations, and we don’t cut any services. In my book, the work you all do in your communities is much better than the work the state could ever do,” he said.