ST. PAUL — Short on sleep and time, Minnesota lawmakers today darted toward the finish of a legislative session that produced a hefty tax increase, substantial new investment in schools and a landmark law legalizing gay marriage.

The last hours promised drama as twin Democratic majorities worked to act on must-pass budget bills while squeezing in a smattering of proposals they would like to accomplish before leaving town.

Around 2 a.m., the House narrowly approved the legislation to raise taxes by $2.1 billion, mainly by making smokers and the top 2 percent of income earners pay more. Minnesota’s top income tax rate would be vaulted into the nation’s top five.

“There is no glee or joy in doing the difficult work of raising revenue,” said Democrat Rep. Ann Lenczewski. She framed the vote as a responsible approach to erasing a $627 million deficit and fashioning a two-year budget that makes big new commitments to schools, colleges and other programs.

In a six-hour debate, one Republican after another warned the new taxes would backfire and lead the wealthy to flee. “Money talks and money walks,” said Rep. Peggy Scott, R-Andover.

Passage in the Senate isn’t in doubt, and Democratic Gov. Mark Dayton is on board.

The taxes represent a key link to a new $38.3 billion state budget for the next two years. The only other outstanding portion was a bill to pay for core state agencies, such as the Revenue Department and Department of Veterans Affairs. Both chambers were primed to act on that.

After working deep into the night for several days in a row, Democratic and Republican leaders agreed early Monday to break until lunchtime to let members and staff catch up on sleep. They realized it meant sacrificing a valuable commodity: time.

Democrats reluctantly declared a bill aimed at curbing school bullying a casualty of the dwindling clock. Critical financing for the state Capitol’s ongoing renovation was in limbo. A sizable increase to the state’s minimum wage remained in play, but barely according to top lawmakers. And a bill that could lead to unionization in home-based day cares and among home health care workers threatened to chew up valuable hours as Republicans intent on stopping it came armed with a stack of amendments.

Sen. Scott Dibble, the Minneapolis Democrat pushing for the new bullying policy, complained that Republicans stonewalled his bill by pledging a lengthy debate.

“This is a political agenda and kids lose out,” he said.

Senate Minority Leader David Hann and his fellow Republicans expressed concern it would burden schools with new state requirements and open them up to potential lawsuits.

“Many people in the state frankly don’t think it is needed,” Hann said.

Harmony was more apparent in the Senate on other things. A 43-26 tally sent a proposed constitutional amendment to the 2016 ballot that asks voters if an independent council should set legislator pay; that decision now rests with lawmakers, who haven’t touched salaries since 1999 for fear of a political backlash.

A surprising unanimous vote came on a borrowing measure that would generate $131.6 million for the next phase of a state Capitol fix-up and related parking structure. Hann and Senate Majority Leader Tom Bakk said they were worried about a costly lapse in the project by doing nothing on the financing this year.

“I know a little something about construction,” said Bakk, a carpenter. “It doesn’t make any sense to ask the contractor to leave and pay for the cost of remobilizing to come back here and start up again.”

House Speaker Paul Thissen and House Minority Leader Kurt Daudt said they weren’t sure if their colleagues would go along. The borrowing bill takes a super-majority to pass. The Capitol project was contained in a much-larger construction borrowing bill that was fell a handful of votes short of a passing margin late last week.

A House-Senate conference committee was convening Monday morning to see if it could bridge differences on the minimum wage, which now stands at $6.15 per hour.

What was considered a priority earlier in the year has stalled. The House approved a bill raising it in three stages until the hourly minimum reaches $9.50 by 2015; the Senate’s bill topped out at $7.75. If they agree on a number, legislative negotiators also must decide if the wage will rise by an inflationary amount in future years.

Republicans had little appetite for that bill, which they lump together with the tax plan in their argument that Minnesota is becoming less attractive for businesses.

The tax bill that passed the House 69-65, with a four Democrats joining all Republicans in opposition. It would result in the first state-level tax increase approved by lawmakers since the gas tax went up five years ago.

Some 54,400 taxpayers would pay a higher income tax, averaging $7,200 more per year. The new 9.85 percent upper income tax level is two percentage points higher than the current top tier. The tax on a pack of cigarettes goes up $1.60. Corporations lose some tax preferences. And some businesses see more transactions subjected to the sales tax.

The bill contains $570 million in new credits and local government exemptions that backers frame as property tax relief. Some money flows into aid programs that give breaks directly to homeowners.

Once lawmakers adjourn, they won’t return for their election-year session until late February.