ST. PAUL— Minnesota legislators went into overtime Tuesday to wrap up work on a $46 billion state budget and conclude a nearly five-month session, but slow progress on final spending agreements left lawmakers with no guarantee they’d meet even their extended deadline.

Democratic Gov. Mark Dayton and the Republicans who control the Legislature struck an agreement shortly before midnight Monday — the mandated end of the regular session — on how to use a $1.65 billion surplus. They agreed to put $650 million toward tax relief, $50 million to expand preschool offerings and $300 million to fix roads and bridges.

“I think it really represents true compromise. We’re getting some things we wanted, the governor is getting some things he wanted,” House Speaker Kurt Daudt.  We’re pretty happy with that.”

The Legislature sent Dayton five budget bills before Monday’s midnight deadline, but the outstanding spending packages eat up 85 percent of the state’s overall budget. Though the special session began right at 12:01 a.m. Tuesday, the Legislature remained at a standstill through Tuesday evening as Dayton and Republicans worked to finalize agreements for health care service spending, state agency funding, public school spending, tax breaks and transportation repairs.

Bills released late Tuesday would devote three-quarters of the state’s budget surplus to boosting spending for public schools and tax cuts. An education budget pays to increase the state’s per-pupil funding formula by 2 percent in each of the next two years, while also setting aside $50 million to expand preschool options — a top priority for Dayton.

Initial plans for a $660 million bill of tax breaks shrunk by $10 million in last-minute negotiations. But new tax cuts would be created for college savings plans and tuition debt, Social Security income and first-time homebuyer accounts.

The planned Major League Soccer stadium in St. Paul would get a long-awaited exemption from state and local property taxes. In another move, the bill would also slash taxes on premium cigars — from $3.50 to 50 cents each — and remove inflation-adjusted increases for cigarette taxes that were approved in 2013.

But the Legislature still faced a logistical crunch to get the remaining bills drafted — a process that can take up to 10 hours for some bills — and ready for final votes in both chambers.

It raised the prospect that lawmakers would need yet another extension to finalize the budget.

Senate Majority Leader Paul Gazelka said Tuesday afternoon he was hopeful they could beat the new special session deadline of 7 a.m. Wednesday.

“It looks right now like we’ll get done before 7 a.m.,” Gazelka said.

Dayton had deemed expanding a preschool program launched last year into more schools a must-have in the budget, funding Republicans resisted. And the GOP pushed the Democratic governor for more in tax relief and a transportation funding plan that doesn’t raise gasoline taxes or license tab fees.

Their agreement also calls for nearly $1 billion of public construction projects, with a healthy share earmarked for transportation repairs.

“It’s not everything that I want,” Dayton said of their agreement. “You give and take.”

Special sessions have become routine at the Legislature. Lawmakers needed a one-day overtime session while setting its last budget in 2015 after Dayton vetoed several spending bills.