Last fall, Minnesota voters brought divided government back to the State Capitol. By midnight Monday, they will find out if Democrats and Republicans can run state government efficiently together.

The state’s political leaders headed into the regular session’s last day still at odds over how it should finish. On Sunday afternoon, Gov. Mark Dayton once again promised to veto a $400 million education spending increase agreed to by his fellow DFLer, Senate Majority Leader Tom Bakk, and GOP House Speaker Kurt Daudt. That’s not enough new money to cover Dayton’s top priority, expanded prekindergarten courses at public schools.

“I will veto, again, I will veto a $400 million bill,” Dayton said. A veto would bring high-profile consequences, including the prospect of a Department of Education shutdown, and likely would require a special legislative session to sort out. House Republicans would bear the blame for that, Dayton vowed.

Working through the night -- adjourning at 5:36 a.m. Monday -- the House passed the $17 billion education plan -- with $400 million in new school spending -- that Dayton has vowed to veto. The vote was 71-59.

The Senate had already adjourned for the night, before the House passed the measure. The Senate is expected to take up the bill when it convenes at 9 a.m. Monday.

“I regret the consequences [of a veto], but I regret just as much the consequences of not providing prekindergarten for 40,000 children in Minnesota,” Dayton said. He contended that House Republicans prefer to leave more than $1 billion in state funds unspent in order to push a large tax cut next year.

Following a private meeting with Dayton, Daudt also gave no new ground on the education spending dispute.

“It’s his responsibility to build a groundswell of support for his issues in the Legislature,” Daudt said. “And the fact that that particular issue didn’t make it into the conference committee, it didn’t pass the House or the Senate, makes it a difficult position. I certainly ask the governor to reconsider and not veto the education bill.”

Bakk said late Sunday night he still intended for the Senate to pass the education bill he agreed upon with Daudt. “This is a really good education bill with a lot of money for schools,” Bakk said. In fact, it contains a bigger boost in per-pupil aid payments to school districts than what Dayton is currently seeking. If Dayton vetoes the bill, Bakk said, it will be up to the governor and speaker to negotiate a solution.

Amid high stakes and uncertainty, legislators worked long hours and late nights through the weekend. Sunday brought the start of House and Senate floor votes on billions in state spending, a series of compromise bills filled with barely vetted details.

Dayton said he hasn’t closely examined those bills, and several include provisions that raise the possibility of additional budget-bill vetoes from the governor. A bill funding state courts and public safety programs includes a measure legalizing firearm suppressors, commonly known as silencers, which Dayton earlier in the session said he would veto. It does not include a provision, strongly supported by many DFLers, to restore voting rights for felons.

The higher-education funding package doesn’t include enough new dollars to prevent likely tuition increases at public colleges and universities. The health and human services budget deal authorizes premium increases come Aug. 1 for some higher-earning enrollees in MinnesotaCare, the state’s public health insurance program for low-income people. An environmental budget bill included a plan for clean water protections that were also a top Dayton priority, but which he said Sunday “needs to be improved.”

Dayton said his focus in the last few days has been the education bill, and he declined to offer specific veto threats regarding other budget bills, but neither did he foreclose that possibility.

Bakk and Daudt have promised an on-time finish, which Daudt reaffirmed on Sunday. “We’re going to make it,” Daudt said after his meeting with Dayton.

But the rushed nature of the final days, full of partisan intrigue and dozens of other smaller policy disputes, left considerable uncertainty about whether a special legislative session could be avoided even if Bakk and Daudt are able to hold their own agreement together.

The dynamics of the relationship between Dayton, Bakk and Daudt have shifted throughout the session, which got underway in January. An early public skirmish between the DFL governor and Senate leader gave the Republican speaker an opening to play peacemaker, and he took it.

But the standoff over what to do with the $2 billion budget surplus has Dayton and Daudt straddling a more traditional DFL-GOP divide. Hoping to finish the session on time, Daudt and the House GOP backed off their desire for about $2 billion in tax cuts this year, a plan to eliminate MinnesotaCare, and a significant spending boost on road and bridge repairs.

Democrats and Republicans each proposed hefty transportation spending plans, $11 billion and $7 billion respectively, with the DFL approach relying on a gas tax increase that House Republicans opposed. The GOP advocated a general treasury infusion for roads, to deploy bonding debt for some projects. Daudt and Bakk have signaled that both tax cuts and transportation would be back on the table next year, and lawmakers instead over the weekend brought forward a much smaller transportation bill its sponsors described as “lights on.”

In the final standoff over education, Bakk is positioned between the two, saying he personally supports Dayton’s approach but can’t pull Daudt along.

With every legislator on the ballot in 2016, Daudt, Bakk and their respective caucuses stand to lose politically if an education bill veto produces a long stalemate and instigates a high-profile shuttering of the Education Department.

So far Daudt, who entered state politics as a political strategist, has kept the often unruly House Republican caucus focused on an orderly finish. Twice in the last decade, long end-of-session standoffs followed by government shutdowns contributed to the GOP losing House majorities.

Bakk has little to gain from a protracted dispute with Dayton. Needing to protect his own Senate majority next year, a division in the DFL over education funding could force the party’s donors and power brokers into difficult decisions.

Dayton is more insulated from such electoral pressure, but a contentious partisan standoff at the start of his second and final term could mean long-term consequences for his legislative agenda through the rest of it.

If the current standoff produces a long stalemate over Dayton’s push for more prekindergarten money, the governor said he believed Minnesotans would take his side. “The public will have the opportunity to focus on this in a special session, when it’s not one of a thousand other things going on,” Dayton said. “And the spotlight will be on House Republicans.”

A special session would force difficult decisions about where to hold it, given the planned post-session acceleration of construction activity inside the under-renovation Capitol. Dayton suggested Sunday that lawmakers could hold it in a tent on the Capitol grounds. A spokesman later said Dayton was not kidding about that.

In other action overnight, the House also passed a $12 billion Health and Human Services bill on a bi-partisan 99-31 vote. The House is scheduled to reconvene Monday at 11 a.m., less than 5 hours after it's Sunday-to-Monday marathon session.

-- The Associated Press contributed to this report.