ST. PAUL — Legislative leaders started chipping away at a budget deal on Thursday, finalizing high-level spending numbers for Minnesota’s public universities, courts and public safety programs while leaving larger slices of the state’s $40 billion-plus budget for later.

After more than 24 hours of private talks this week at the governor’s residence that yielded little outside of vague promises of progress, smaller pieces of a wide-ranging budget deal started falling into place. In a sign of what’s to come as the Legislature races toward its Monday deadline, the total spending number released for those programs was higher than House Republicans aimed for and lower than in Senate Democrats’ budget.

In one of a few prolonged interviews top negotiators have given since negotiations ramped up Monday, Senate Majority Leader Tom Bakk tried to lower expectations Thursday evening for doling out the state’s nearly $1.9 billion surplus. He noted the deal struck with Republican House Speaker Kurt Daudt and Gov. Mark Dayton on higher education wouldn’t provide enough money to freeze tuition at all state institutions.

“There’s just not enough money to avoid (tuition increases),” the Cook Democrat said. “We’re having to be much more conservative I think than a lot of the different advocacy groups had hoped.”

Other more contentious negotiations over larger chunks of the state budget are still in flux. Legislative leaders met for more than five hours Thursday, moving to health and human services funding and other budget areas. Negotiators planned to resume talks Friday morning.

Bakk said the trio hadn’t yet discussed two of the biggest items still up in the air: House Republicans’ plans for $2 billion in tax relief and Democrats’ gas tax-backed funding package for road and bridge repairs. He mentioned the possibility of a special session to tackle those issues but called such a move unlikely, given renovations that will consume the Capitol after Monday’s adjournment.

With a few deals in place, the work will shift back the Capitol to iron out smaller differences and pass budget bills onto the governor. For instance, it will be up to a team of lawmaker from the House and Senate to dole out the money to college and university systems, determining which schools may see tuition increases over the next two years.

Sen. Ron Latz, DFL-St. Louis Park, said the agreement on funding for courts and public safety provides for back-to-back 4 percent compensation increases for judges and judicial branch staff, who had seen five years of pay freezes during Minnesota’s lean budget times. It will also guide $11 million in new money into the Bureau of Criminal Apprehension for new forensic lab equipment, fingerprint and DNA analysts and other investigative staff. And he said the sides agreed to put $10 million into an emergency account that could be tapped when natural disasters hit.

Some rank-and-file lawmakers sounded the alarm Thursday about a looming time crunch for the grunt work of passing budget bills before midnight Monday.

Sen. Julie Rosen, a Vernon Center Republican and one of the 10 health policy negotiators, predicted it would take three days for bill writers and legal staff to assemble a health and human services bill that stacks up to 5 or 6 inches tall.

“Members, we are going into special session unless we have a deal on the table right now that we can get into conference committee,” she said.

But Rep. Denny McNamara wasn’t worried about running out of time. As the House adjourned for the day around 3 p.m., the Hastings Republican looked at his watch and tried to calculate the number of hours until the mandatory end — guessing about 100.

“That’s a legislative eternity,” he declared.