Divided government is back at the State Capitol, after Minnesota voters defied a national Republican wave to re-elect Gov. Mark Dayton but also gave him a new Republican House majority.

"It's a prescription for gridlock unless we can all rise above that and do it better," Dayton said Wednesday, in his first public appearance since claiming victory the night before against Republican challenger Jeff Johnson.

By handily winning their re-election battles, both Dayton and Sen. Al Franken avoided the fate of many Democrats running for U.S. Senate or governor across the country who fell to Republicans ­Tuesday night.

But both men now face harsh new political realities: Dayton must grapple with a House Republican majority, while Franken, after a first term in a Democratic-controlled U.S. Senate, will come back in the minority.

"Believe me, there's going to have to be a lot of work across party lines," Franken said Wednesday, the day after he easily won re-election by dispatching Republican challenger Mike McFadden.

Franken said he planned to reach out to his new Republican colleagues with phone calls and mentioned how he's struck up good working relationships with Republican senators like Rand Paul of Kentucky and Orrin Hatch of Utah. Even with the 2016 ­presidential race soon to heat up, Franken said he thought the two parties could find common ground on such issues as transportation, infrastructure improvement and foreign policy.

In Minnesota, the new political alignment will be tested immediately when lawmakers gather in St. Paul in January. Passing a state budget will be job No. 1, and the first goal for both parties is to avoid repeating what happened the last time Dayton and Republicans shared power: a 21-day state government shutdown in 2011.

"I don't see any reason why we'd have one, and I hope the Democrats don't want one, either," said House Republican Leader Kurt Daudt of Crown, who on Friday will find out if his GOP colleagues will select him as the next speaker of the House.

Avoiding shutdown

The state's financial condition could go a long way toward avoiding another shutdown. State government has been running a small surplus, meaning Dayton and legislators won't be forced to make deep spending cuts — or look for major new sources of revenue. A state budget forecast in early December will give Dayton and lawmakers a ­better idea of the fiscal situation they'll face in January.

The debate over taxes vs. spending cuts was at the heart of the 2011 shutdown. That year, Dayton took office along with new Republican House and Senate majorities, facing a $6 billion budget deficit. While Dayton sought a mix of spending cuts and tax hikes to cover the gap, Republicans united to oppose any tax increases.

The ensuing stalemate ended only after Dayton agreed, three weeks into shutdown, to a Republican proposal to avoid deeper spending cuts by delaying payments to schools and borrowing against future revenue from the state's 1998 settlement with tobacco companies.

This year, Dayton said, "I don't want to be confrontational. I want to see what their priorities are. I'm willing to look at anything and talk about anything and think about anything."

'Dayton unbound'

Even as he sounded a conciliatory note, Dayton said he would expect Republicans to show they are willing to compromise. Democrats have a better hand than they did in 2011, with the party continuing to control the state Senate.

"I'm not going to meet them all the way. I'm not going to give up everything I believe in," the governor said. Having won what he has said would be his last campaign, Dayton also joked about the possibility of taking a more blunt approach in his second term.

"I'll be Dayton unbound," he said.

Daudt, who held a Capitol news conference Wednesday with several dozen new and returning House Republicans, provided few specifics on goals or priorities for the group. He said that would be worked out in the coming weeks.

At the event, Daudt avoided confrontation. Asked if House Republicans would seek to repeal MNsure, of which they have been extremely critical, Daudt said that didn't seem like a realistic goal, although he said the new majority was interested in taking a much more active oversight role in managing the health ­insurance exchange.

"We're working with a Democrat governor and a Democrat Senate," Daudt said. "I'm not going to draw a line in the sand and say we're not going to do A, B or C."

Roz Peterson, a new Republican House member from Lakeville, said she felt compelled to listen to the many frustrated voters she encountered while on the campaign trail.

"I heard time and time again that people didn't feel their voices are being heard in St. Paul," she said.

Besides the budget, another test for the two parties will be a likely push for a boost in transportation funding. ­Dayton called it a top priority, and Daudt said Republicans are ready for the discussion, too. Recent state analyses have found Minnesota's transportation funding is failing to keep up with a deteriorating infrastructure, but Democrats will face an uphill battle in convincing GOP lawmakers to raise any transportation-related taxes in order to pay for new projects.

Senate Majority Leader Tom Bakk, DFL-Cook, said transportation funding would be among the first topics he discusses with the new House speaker. Bakk was Senate minority leader in 2011 and led his party to the majority in the 2012 election that saw Republican losses that some in the party blamed on the shutdown.

"I think the Republicans are going to be careful," Bakk said. "I have to believe that there are enough of them left that went through 2011, that really overreached and shut government down. It swung back on them hard. I think they'll be careful to not be that rigid again, for fear of that pendulum coming back on them again."

Staff writer Allison Sherry contributed to this story.

Patrick Condon • 651-925-5049