The General Assembly likely won’t adopt the next state budget until the final week of the regular 2023 session, but House leaders remain confident a bipartisan deal will be enacted before adjournment June 7.

House Speaker Matt Ritter, D-Hartford, said during a mid-morning press conference Wednesday that negotiations with Gov. Ned Lamont’s administration are winding down, but a few minor items remain unresolved.

One involves a municipal assessment for trash-to-energy plant services, he said. A second, according to sources close to the talks, involves payments for financially distressed hospitals.

The budget debate will probably begin in the House, as it does most years, and Ritter said leaders still are considering coming into session Saturday. “We haven’t taken that off the table,” he added.

Otherwise, the House likely would vote on the budget Monday.

In either event, a Senate debate and vote on the next two-year fiscal plan for the state wouldn’t occur until next week.

Still, Ritter said he’s confident a deal will get done before the session ends at midnight June 7, especially with Democratic and Republican leaders both aiming for a cooperative deal.

“The nice thing about the budget is we anticipate a bipartisan budget,” the speaker added. “That still looks very good. And so you don’t have to worry about the clock running out.”

House Minority Leader Vincent J. Candelora, R-North Branford, told the CT Mirror on Wednesday he also is “cautiously optimistic” that the budget will be resolved on time.

“I think it would be irresponsible for us to go into special session given where we are financially,” he said.

Legislative leaders and Lamont have been talking optimistically about a budget deal for the past three weeks, pledging the package would be centered on the first state income tax rate cut since the mid-1990s — a plan expected to deliver hundreds of millions of dollars of annual relief to Connecticut’s middle class.

But reaching agreement also has proved challenging because of the state’s spending cap, which tries to keep appropriations in line with inflation and household income.

Progressives among the Democratic majorities in the House and Senate argue the cap doesn’t allow sufficient growth to protect core services harmed in recent years by inflation and by the economic chaos of the coronavirus pandemic.

Throughout much of the cap’s history, allowable growth hovered around 3%. But because of the 40-year-high in inflation reached last June, when the Consumer Price Index topped 9%, allowable growth in the first year of the new biennium is close to $1 billion, according to Lamont’s budget office. That’s more than 4% of the current General Fund.

Critics particularly have questioned whether the new biennial budget will provide sufficient funding for public colleges and universities, grants for local school districts, and state-sponsored social services delivered by nonprofit agencies. Labor leaders also fear the new budget will continue a long-running trend of shrinking state agency staffing.

Labor groups have been increasing the pressure on legislators recently to invest more in core state programs.

Striking group home workers demonstrate daily outside of the Capitol, and leaders announced that union members would engage in “peaceful civil disobedience” Thursday.

“Governor Lamont’s continued lack of awareness of the crisis in Connecticut is a choice,” labor leaders wrote in a statement. “He’s choosing to ignore the 1,700 striking long-term caregivers in Connecticut’s group homes and the 11,000 home care providers funded through Medicaid.”

The administration has said it’s the responsibility of the union and the nonprofit organizations that run the group homes to reach a fair new contract. Lamont also has said budget critics have lost perspective, and that while funding increases may not be as great as some want, the new budget invests more in most key areas.

Leaders of higher education faculty unions joined those demonstrating group home workers early Wednesday afternoon outside of the Capitol.

“The harm that will be done to our system by the proposed budget will be felt acutely by our students, their families, and our communities first,” said Seth Freeman, President of the Congress of Connecticut Community Colleges. “But the long-term effects will impact Connecticut for decades as the disinvestment in [the state college and university system] will widen the educational inequality gap that exists between white students and Black and Brown students.”