HARRISBURG — Final details were being ironed out Thursday on a $27.15 billion budget agreement between Gov. Tom Corbett and top lawmakers that is expected to cut spending by about 3 percent and deliver deep cuts in aid for public schools and state-supported universities.

Senate Majority Leader Dominic Pileggi, R-Delaware, said there is an agreement on many parts of the budget and that he hopes the rest will be resolved in time for a budget bill to be presented on Sunday in the chamber’s Appropriations Committee.

“We have a framework in place,” said Pileggi, R-Delaware. “We have certainly an agreement in principle, if you want to call it that, and we’re working through the details.”

The plan under consideration would cut spending about 3 percent from this year’s $28 billion budget as Corbett and his fellow Republicans who control the Legislature have scoured state government for cuts in an effort to fill a projected multibillion-dollar budget hole without raising new taxes.

Pileggi declined to discuss details, and cautioned that until all matters are settled, “no part is really set in concrete.” Pileggi and other budget negotiators are working against the deadline of July 1, when the new fiscal year begins, and have repeatedly said they intend to enact the budget on time.

Senate Appropriations Committee Chairman Jake Corman described a $27.15 billion budget framework that includes small changes to a budget bill that passed the House last month.

That bill would cut more than $1.1 billion in aid to public schools and 18 state-supported universities while seeking about $470 million in savings and reductions from the wide array of social and human services in the Department of Public Welfare’s $11 billion budget.

“We’re down to the final pieces here. It’s pretty solid,” said Corman, R-Centre.

One item still under discussion is the amount of aid that hospitals will receive for their role in caring for the poor or uninsured, Corman said.

House leaders made no announcement. Earlier, Corbett said at an afternoon news conference Thursday that he would not disclose terms until a handshake deal is made.

“Work is still being done, but I have confidence that we will have a budget on time,” Corbett said.

Corbett, in his first six months as governor, believes the budget plan under construction will allow him to keep promises he made during his campaign last year not to raise taxes or fees, a spokesman said.

However, one anti-tax group, the Washington, D.C.-based Americans for Tax Reform, whose pledge Corbett signed during the campaign, complained Thursday about the possibility that lawmakers would increase an assessment on hospitals in Pennsylvania — a prospect that would save money for both the state government and the hospitals by securing more federal Medicaid dollars.

Democrats have not been included in budget talks and have criticized Republicans’ insistence on cutbacks in government spending. The state has hundreds of millions of dollars more in surplus money that it could use to ease the proposed cuts, which will inflict long-term damage on Pennsylvania’s economy, quality of life and social safety net, Democrats contend.

In the meantime, public school districts faced with drop-offs in state aid, especially the state’s poorest, are preparing to lay off teachers and other employees, close school buildings, raise property taxes and eliminate programs such as full-day kindergarten.

Pileggi had described Thursday as the deadline to get a handshake agreement with Corbett to allow sufficient time to write bills and hold votes to enact a budget before the new budget year starts at the end of next week.

In general, the closed-door negotiations were said to revolve around the level of aid for public schools, universities, hospital care for the poor and social services.

Republican lawmakers had pressed Corbett to relent on his initial proposal in March for more than $1.6 billion in cuts to state-supported universities and public schools, while Corbett wanted lawmakers to back down on social services spending cuts proposed in the House bill.

With the House and Senate scheduled to be in session nearly every day through June 30 before lawmakers take their traditional two-month summer break, Corbett is pressing them to approve legislation to create school vouchers, limit the exposure of defendants to civil court damage awards and expand the ability of schools to lay off employees.

“There is a large amount of legislation that is out there,” Corbett said. “The No. 1 thing that has to be passed, obviously, is the budget.”