DoweJones

The agreement came after a three-hour negotiating session that followed Dayton’s announcement of his offer earlier in the day. If details are worked out and approved by state legislators, it would end the shutdown over how to resolve a $5 billion deficit that has lasted two weeks.

Dayton said the government would be back in business very soon but did not say exactly when.

The two sides agreed on a proposal that would raise $1.4 billion in new revenue, half by delaying state aid checks to school districts and the other half by selling tobacco payment bonds. It was a big sacrifice by Dayton, who had made new income taxes a central plank in his campaign last year and the centerpiece of his budget.

Republicans said they agreed to drop a list of policy changes and a plan to cut the state workforce by 15 percent.

“It was about making sure that we get a deal that we can all be disappointed in, but a deal that is done, a budget that was balanced, a state that was back to work,’’ said House Speaker Kurt Zellers, a Republican who appeared with Dayton and Senate majority leader Amy Koch after the private meeting.

The glum looks on their faces testified to a hard bargain.

“Nobody is going to be happy with this, which is the essence of real compromise,’’ Dayton said.

The date of a special legislative session to pass a budget and end the shutdown has not been set. Some terms of the deal still need to be filled in.

The shutdown has idled 22,000 state employees, closed state parks and rest stops, and cut off funding to many social services. It has cost the state millions in the cost of preparing for the shutdown and in lost revenue since then.

The deal is contingent on approval by the Legislature, no easy task after an election in which a more conservative Republican caucus took power. Koch and Zellers said they believed rank-and-file legislators would approve it. Republicans hold narrow margins in both chambers, and Democratic minority leaders weren’t in on the deal-making.