ST. PAUL — Minnesota lawmakers on Thursday hoped to close out what was meant to be a one-day special session on Day 3, as the House and Senate worked to pass the remaining spending bills to put the finishing touches on a $46 billion two-year budget.

The overtime work has been slow going at the Capitol, where Gov. Mark Dayton and legislative leaders got hung up on the final details of a broad budget agreement that would put $650 million toward tax relief, expand preschool offerings by $50 million and dedicate $300 million to fix roads and bridges. After missing Monday’s constitutionally mandated deadline to adjourn without finishing the bulk of a new budget, the Legislature immediately entered a special session — only to miss its self-imposed goal of wrapping up by 7 a.m. Wednesday.

And the path looked to get tougher when the Legislature resumed Thursday morning. Two Republican senators were gone, leaving the Senate short the votes it needed to pass budget bills.

But Senate Majority Leader Paul Gazelka confirmed they would remove changes that angered Democrats over how union labor contracts are ratified from a financing bill for state government agencies. Its removal won over critical Democratic votes to pass the bill.

The Legislature was expected to continue holding final votes on remaining budget bills throughout Thursday night, and Gazelka said he was confident the Legislature could finish the remaining measures overnight.

“It feels like the final approach,” he said.

That resolution appeared to break a logjam that kept the Legislature largely at a standstill throughout the week. Within minutes of passing the state government budget, the Senate quickly approved a budget for public schools with money to increase the per-pupil funding formula by 2 percent in each of the next two years and additional money for preschool, one of Dayton’s top priorities.

Also on the agenda was a bill that would have the state borrow more than $1 billion for public construction projects, including more than $250 million for transportation infrastructure. The so-called bonding bill was expected to be the final piece of legislation that lawmakers take up during the special session, which was originally supposed to end by 7 a.m. Wednesday.

The bill also includes nearly $120 million for the University of Minnesota and over $92 million for the Minnesota State Colleges and Universities system.

The bonding bill’s funding for road and bridge repairs, a critical part of a deal struck between Dayton and Republicans that also puts $300 million of the state’s surplus toward transportation funding. Republicans billed it as the first significant infrastructure package in nearly a decade and one that doesn’t raise gas taxes or license tab fees — a fact that led Democrats to brand it as falling far short.

“I think, frankly, this is a pretty big deal,” said Sen. Scott Newman, the state’s Transportation committee. “We are pretty close to passing a transportation bill with some new money.”

One of the largest outstanding pieces of the budget was funding health and human services programs, which wasn’t released until late Wednesday night. It would make more than $450 million in cuts to the state’s spending on health care services, but also angered conservatives because it tries to limit the pain of those cuts by emptying a dedicated health care account to cover some of those costs.

The bill also includes numerous fee hikes for people and businesses such as chiropractors, hearing aid distributors, manufactured home parks, tattoo artists and body piercing shops.

The Legislature sent Dayton five budget bills before the regular session ended, but the state could plunge into a partial government shutdown unless lawmakers put the final spending pieces together before July 1. Even then, it wasn’t clear whether Dayton would sign all 10 bills.

Gazelka said the two sides were trying to find a compromise that the governor would approve. But at least one bill was destined for a sure veto.

The Legislature on Thursday sent Dayton a mix of labor measures he wanted — like increased pension funds, extending parental leave for state employees and ratifying union contracts — and one that met his ire: barring local governments from passing their own minimum wages or sick leave policies. Dayton vowed he would strike it down.