ST. PAUL — The final hours of Minnesota’s legislative session slipped away Monday without any sense of finality because lawmakers will leave without a budget deal and must return at Gov. Mark Dayton’s call to solve a $5 billion deficit.

A stubborn dispute over taxes and spending kept the session in a holding pattern in recent weeks.

Instead of a last rush of activity to finish by the midnight deadline, the GOP-controlled Legislature plodded along, debating issues such as civil lawsuits and the distribution of dedicated funds to outdoors and cultural programs.

Dayton, a Democrat, dampened the mood even more by saying he doesn’t intend to begin vetoing the Republicans’ budget bills before Tuesday. Legislative leaders held out hope that he would sign the bills or veto them quickly so they could send him do-over versions.

“This is a shared failure on all our parts, the Legislature’s and mine, that we can’t reach resolution,” Dayton told Capitol reporters.

The clash between Dayton’s quest for new high-end income taxes and Republicans’ insistence that the state has enough money has pushed Minnesota closer to a government shutdown starting on the July 4 holiday weekend. The current two-year budget runs through June 30. Without a new budget, appropriations for most of what the state does would stop July 1.

Republican lawmakers gathered outside Dayton’s office three hours before midnight to demand one last time that he sign their budget bills. But even Senate Majority Leader Amy Koch acknowledged the likelihood of a special session, forecasting what would happen if the deadline passed without a deal.

“We will continue the conversation with the governor,” said Koch, R-Buffalo.

Dayton and Republican leaders had not met for several hours by the time of the nighttime Republican news conference.

The only piece of the state budget enacted so far is a slender $76 million package for farm programs, which Dayton signed last month.

The governor said he will likely wait to reach a budget deal with Republicans before calling a special session. He said he hadn’t considered whether that would be before or after a shutdown started, if there’s no agreement beforehand.

Dayton insists that he moved toward Republicans a week ago when he reduced his proposal for new taxes by about half to $1.8 billion, raised mainly from a new tax bracket for the top 2 percent of incomes. GOP lawmakers said they already compromised within their ranks by agreeing to spend $34 billion, the amount the state is projected to collect in the next two years, even though some wanted a smaller number.

“I would have preferred to spend a little bit less, yes,” said Rep. Doug Wardlow, a first-term Republican from Eagan. “We have moved in the direction of the governor significantly — substantially.”

Dayton and top GOP lawmakers hadn’t met on Monday, after closed-door meetings in recent days without much progress. The governor continued a series of private meetings with legislative sponsors of the spending bills and the tax bill.

House Taxes Committee Chairman Greg Davids said his meeting Monday was “substantive” but didn’t lead to any breakthroughs on the larger disagreement. He said Dayton’s tax plan doesn’t have the votes to pass the Legislature.

“He can’t get the 68 votes. I know he can count to 68 but he can’t get there,” said Davids, R-Preston, referring to the number of votes to pass a bill in the House.

Dayton said he is open to alternative ways to bring new revenue into the state budget.

“But nothing that’s been proposed here in the last five months has come even close to raising that kind of money,” he said, referring to the $1.5 billion his proposed 10.95 percent income tax bracket would bring in over two years.

A minor flap over religion developed Monday, when Democratic Senate Minority Leader Tom Bakk used the word “cult” in describing the new Republican majorities. It demonstrated the frustration and tempers that often arise in the final hours of a legislative session.

“Their principles are so burned into their soul that it’s almost like a religion, like a cult,” Bakk, DFL-Cook, told reporters. “You can’t compromise on that. And I think that’s problematic for the Legislature going forward.”

Two Republican senators responded in a hastily arranged news conference, where Sen. Dave Thompson called the comment “bizarre” and “unhelpful.”

“I am not ashamed of the fact that I want to maintain fiscal discipline for the citizens of the state of Minnesota,” said Thompson, a first-term Republican from Lakeville.