The tragedy in Newtown became part of the deficit-mitigation debate late Monday as some legislators questioned suggested reductions to state agencies serving people with mental illnesses and those with developmental disabilities.

And though no final decisions on legislation to address the deficit are expected before Wednesday’s special session, those who brought questions to the House Democratic Majority Caucus Monday said they expect lawmakers to scrutinize these segments of the budget very closely over the next two days.

“Obviously this was an individual with mental issues,” Rep. Catherine F. Abercrombie, D-Meriden, said of Adam Lanza, the 20-year-old who fatally shot 26 students and staff at Sandy Hook Elementary School Friday. Lanza, who took his own life, is also believed to have shot and killed his mother before the events at the school.

Abercrombie, who is vice chairwoman of the Appropriations Committee and also serves on the legislature’s Public Health panel, was careful — as were her colleagues — not to form any conclusions about reductions suggested several weeks ago for the Department of Mental Health and Addiction Services or for the Department on Developmental Disabilities.

But at a time of heightened concern about the challenges these agencies face, Abercrombie predicted that lawmakers would focus intensely on any potential cutbacks in these areas.

“It’s obvious he (Lanza) did not get the services he needed,” she said.

Rep. Patricia Dillon, D-New Haven, another veteran member of the Appropriations Committee, said state officials have known for more than a decade that as psychiatric hospitals have closed, community-based providers haven’t received sufficient state funding to meet the increased demand for their programs.

“I think that’s a legitimate question,” Dillon said before entering Monday’s closed-door caucus to discuss a tentative deficit-mitigation agreement. The plan was reached over the weekend between legislative leaders from both parties and Gov. Dannel P. Malloy’s administration. “The private providers don’t have adequate funds,” she said.

An official with the state’s largest health care workers’ union, who spoke with lawmakers before Monday night’s caucus, said further cuts to the state’s support network for people with mental illnesses, addiction issues or developmental disabilities likely would shrink community-based programs that already can’t meet the current needs.

“There’s nowhere further to go,” said Jennifer Smith, legislative director for District 1199 of the New England Health Care Employees Union.

The administration is projecting a $365 million shortfall in the current budget. The governor used his limited authority to unilaterally reduce segments of the budget last month, saving about $124 million.

And in early December he proposed another $240 million in savings, $220 million of which were spending cuts.

The unilateral cuts shaved about $29 million off the budgets for departments serving the mentally ill, those facing addiction and the developmentally disabled. The second round of proposed reductions would take away another $7 million.

Combined, these cuts target just 1.4 percent of this year’s budget from Mental Health and Addiction Services, and 2.6 percent from Developmental Disabilities.

Full details on the tentative deficit-mitigation plan were unavailable late Monday.

But Rep. Peter Tercyak, D-New Britain, said legislators just need to know precisely what effect these potential reductions might have.

“I don’t believe that’s where we’re going to end up,” Tercyak, who co-chairs the Human Services Committee and also serves on Public Health, said of $36 million in potential cuts. “It is getting attention.”

Malloy told Capitol reporters Monday afternoon that the deficit-mitigation plan is a tentative one. And though he wasn’t asked, nor addressed, any specific components, he said, “It’s capable of being adjusted further.”

But earlier in his briefing with reporters, the governor said the nature of Lanza’s actions clearly showed a disturbed mind — a situation that obviously would raise concerns among many in government.

“Are we doing enough from a mental health perspective to reach out to kids who are in trouble and their families?” Malloy asked. “My sense is, we do not.”