Georgia House and Senate leaders agree on most of the big stuff in next year’s $20.8 billion budget: about $300 million extra for schools, more money to help fix the state health insurance program for teachers, employees and retirees, and upwards of $1 billion in new construction projects.

But senators later this week will approve a spending plan for fiscal 2015 — which begins July 1 — that leaves plenty of room for negotiation as the session heads for a March 20 finale.

As is typical, the budget approved by the Senate Appropriations Committee Tuesday cuts some of the projects near and dear to House leaders and puts agencies, such as the University System, on notice that they will have some lobbying work to do before the session ends.

“It’s all doable,” said Senate Appropriations Chairman Jack Hill, R-Reidsville, who has been in the middle of late-session budget negotiations for more than a decade. “The big important things are all handled.”

But in legislative budgeting, it is often the little things that trip lawmakers up.

Legislators have to pass a budget before the end of the year. The document will provide for the education of about 2 million students, plus health and nursing care for more than 1.6 million people. It funds road improvements and prisons, economic development initiatives and cancer research, business regulation and water and sewer projects.

The House passed a budget plan last month, and the Senate will do the same Thursday. The sides agree on a vast majority of the spending Gov. Nathan Deal proposed in January.

They back Deal’s proposal to send schools more than $300 million extra to help reduce or eliminate furlough days for teachers, shrink class sizes and give raises. They also support providing extra millions to allow agencies to offer merit raises to state employees.

They’ve padded Deal’s proposed borrowing for construction projects, bringing the total to more than $800 million. Much of what they added are college facilities and libraries in the districts of top lawmakers. The new Senate plan, for instance, adds county library and college library renovation projects worth about $5.7 million in the district of outgoing Senate Majority Leader Ronnie Chance, R-Tyrone.

Both chambers included language in the budget telling the Department of Community Health to offer 650,0000 teachers, employees and retirees on the State Health Benefit Plan a choice of health care providers, something they aren’t getting now. Members have complained that changes in the plan at the start of this year left them paying dramatically higher out-of-pocket costs and forced them to use a single health insurance company, Blue Cross and Blue Shield of Georgia.

Both chambers added money in the budget to reduce some of the high out-of-pocket costs.

The Senate budget cuts funding for school nurses by about $728,000, a move aimed at forcing local districts to pick up more of the cost of their health coverage.

Senators also cut $15.5 million from the University System in two key areas that are certain to spark debate.

The Senate argues that the system should have saved $7.5 million when it merged some schools last year. University System Chancellor Hank Huckaby said those savings were being plowed back into college programs. However, Lt. Gov. Casey Cagle, the Senate’s president, wants the mergers to save the state money.

Another $8 million would be cut by forcing system presidents to grant fewer out-of-state students waivers so they pay lower tuition. In December, a state audit found that the University System of Georgia waived about $106 million in out-of-state tuition during the 2012-2013 school year.

The Senate also cut $900,000 meant to start up a business incubator program at Kennesaw State University. The school’s chief patron in the House is Rep. Earl Ehrhart, R-Powder Springs, chairman of the higher education budget subcommittee. The Senate also cut in half the number of new family medicine residency slots at Houston Medical Center in the home county of House Majority Leader Larry O’Neal, R-Bonaire.

Meanwhile, the Senate gave House negotiators a fat target of their own by putting $10 million into a new capital venture fund to help tech start-up companies, a pet project of Cagle’s.

House Appropriations Chairman Terry England, R-Auburn, said after the Senate committee’s vote that he hadn’t thoroughly reviewed the other chamber’s budget. But he also made it clear he knew what the Senate had cut.