TRENTON — Secretaries and custodians who recently lost jobs in the Kingsway Regional School District may soon be hired back if lawmakers and Gov. Christie agree on a deal that would portion out extra aid to some districts around the state.

"For the first time in a very long time, I'm optimistic," Superintendent James Lavender said Thursday.

His Gloucester County district would get an additional $820,000 in state aid — a 9.2 percent increase — under an agreement reached Wednesday by New Jersey's top lawmakers, who had been in a stalemate over how to address a chronic funding shortfall and imbalance in distribution of aid among the state's public schools.

In Burlington County, meanwhile, Michael Harris was considering technology and STEM lab investments that he might have to cut.

"We're a pretty big loser," said Harris, superintendent of the Southampton Township School District, which could see a $200,000 — or 9.3 percent  — decrease in state aid in its $13 million budget. "We're frustrated."

The deal to send an additional $146 million to districts like Kingsway, which has been underfunded by the state for years, is contingent on shifting $46 million from districts that receive more aid than the state funding formula says they should, such as Southampton Township. The remaining $100 million will be found within the fiscal 2018 state budget. In February, Christie proposed $35.5 billion in total spending.

It also depends on Christie. The Republican governor, who has line-item veto power over the state budget, expressed some reservations Thursday.

"The governor is willing to consider the proposal, but he has some concerns about fairness," spokesman Brian Murray said.

Lawmakers must pass a budget by June 30 for the next fiscal year. Senate President Stephen Sweeney (D., Gloucester) said Thursday that they would not do so until they came to an agreement with Christie on school funding.

"This is something that's worth fighting over," Sweeney said at a Statehouse news conference. "Obviously, he gets a say in this, too, if we want to get it signed."

Sweeney and Sen. Paul Sarlo (D., Bergen), the Budget Committee chairman, said the proposal, which would also add $25 million for expanded preschool programs, was the start of a multiyear process that would correct inequities in how the state awards aid and ramp up funding to schools through the state's funding formula.

Some GOP lawmakers complained Thursday that schools in Democratic-led legislative districts would benefit more under the plan than those led by Republicans.

Sarlo said there was "no favoritism" behind the proposed aid changes. "It's just straight-up running the formula," he said.

The formula, passed in 2008, calculates how much state aid districts should receive based on the local community's property-tax base and the needs of students in the district.

But it hasn't been funded. If the state were to fully fund districts under the formula and account for enrollment growth, it would cost close to an extra $2 billion, Sweeney said Thursday.

He argued the state can fill that hole if it adds funding each year — and raises new revenue.

On the day a new governor replaces Christie in January 2018, lawmakers will introduce a millionaires' tax, Sweeney said. He said that levy would raise an additional $600 million.

The state also must draw down so-called adjustment aid, Sweeney said — money that was awarded to districts to ensure they didn't lose funding under the 2008 formula, but that was intended to be temporary. Sweeney said that aid totals about $600 million.

"It was a political reality, in order to get the necessary votes," Sarlo said of adjustment aid.

But the proposal to take it away is drawing blowback.

The new funding plan "helps many students in New Jersey, but it does so at the expense of other New Jersey students, which makes the cost too high," Wendell Steinhauer, president of the New Jersey Education Association, said in a statement.

The teachers' union "will not stop fighting to protect every student, in every district, from Steve Sweeney's sick scheme," Steinhauer said.

The New Jersey School Boards Association also expressed opposition to the proposed cuts, though less vehemently.

"While we support the legislative leadership's goal to help underfunded districts, we cannot support a reduction in aid for any school district, particularly at this stage of the budget cycle," the association's executive director, Lawrence S. Feinsod, said in a statement. Districts finalized their local school levies last month, Feinsod said.

Of the NJEA, Sweeney said: "When districts are laying off teachers and teachers are winding up with 35 kids in a classroom, I don't hear the screams of unfairness."

The proposal would cap cuts to districts next year at 1.5 percent of their budgets. "We took a small percentage out of districts that are overfunded, because we don't want to hurt them," Sweeney said.

Harris, in Southampton Township, said the proposed $200,000 cut to his district would be "painful" and questioned why some other districts weren't cut.

For Lavender, at Kingsway, the $820,000 slated for his district wouldn't entirely reverse recent budget cuts — or cover what it's owed under the formula.

"Nobody ever thought I was going to receive a check for $10 million today," he said. But a potential infusion now "really helps us meet immediate needs."