Gov. Mark Dayton ripped House Republican leaders Friday after what he said was a disappointing day of negotiations aimed at resolving a state spending stalemate that has raised fears of another partial government shutdown.

"We went backwards this morning," Dayton said late in the afternoon, after a day of private talks with GOP House Speaker Kurt Daudt and Majority Leader Joyce Peppin following the governor's veto last week of three major budget bills. The DFL governor said he once again offered to surrender what had been his top spending priority this year: a big chunk of new money for public schools statewide to offer prekindergarten courses.

Despite that, Dayton said, Republicans won't agree to about $50 million more he wants spent on schools. Instead, they threw several education policy issues onto the negotiating table that are unpopular with most DFLers: a demand to scrap the seniority-based "last in, first out" policy that governs teacher layoffs and the repeal of a recent Minnesota State High School League policy that gives transgender student athletes access to locker rooms of their choosing.

"It's like we talk different languages," Dayton said of Republicans.

He added: "They consider investing new money in young children something they need something in return for."

Dayton said he is open to resuming talks this weekend, but only if Republicans change what they are offering. Otherwise there is no point, he said.

Daudt was more upbeat after Friday's talks broke up, saying progress was still being made. He expressed continued optimism about a spending deal and ensuing special session as early as next week.

"I think we had another good day," Daudt said before Dayton's remarks.

House Republicans later released details of their Friday offer to Dayton, noting that they have been willing to move closer to Dayton's desired level of education spending increase than he has been willing to move toward theirs.

"We're hoping he moves a little more on education, let's just say," Peppin said.

As the political skirmishing continued, the Minnesota Management and Budget office is preparing for the possibility that it won't be settled by July 1. That's when the state's current fiscal year ends, and it's the point at which seven major state agencies — along with a handful of boards, commissions, schools and offices — would be left with no operating funds going forward unless new budget bills are passed by then.

On Monday, the agency is sending a 30-day warning of layoff notices to 9,451 state government employees. A few of those workers won't be laid off in the event of a July 1 shutdown, since exceptions traditionally have been made for jobs deemed critical to public health and safety.

Those who aren't retained would be eligible for unemployment benefits for the length of the shutdown. During the last partial state shutdown, in 2011, some 22,000 workers laid off for about three weeks did not receive back pay for the hours they lost.

"I don't know what's going to happen. I may or may not have a job come the end of the month," said Andrea Hansen, a 37-year-old Golden Valley resident who works as an education specialist at the Minnesota Department of Education. Hansen's husband works, but she said that if the layoff lingers, she'd likely have to find temporary work in order to cover their mortgage and student-loan payments.

"I cannot afford to be laid off," said Hansen, who is active with the Minnesota Association of Professional Employees, a state worker union whose membership would be hardest hit by layoffs.

Minnesota Management and Budget Commissioner Myron Frans said his agency was not yet able to release data about where geographically the layoffs would fall, but he said the Twin Cities, where most state agencies are headquartered and most state workers are concentrated, would be the hardest hit.

The biggest agency affected is the Department of Natural Resources, with 4,294 of its employees due to receive the layoff letters. The other large agencies affected would be the departments of Employment and Economic Development, Agriculture, Labor and Industry, Education and Commerce, and the Pollution Control Agency.

The rest of the employees work at the Perpich Center for Arts Education, State Academies for the Blind and Deaf, Board of Animal Health, Board of Water and Soil Resources, Office of Tourism, Public Facilities Authority, Workers' Compensation Court of Appeals, Public Utilities Commission, Bureau of Mediation Services and the state technology office, MN.IT Services.

Both the governor and the speaker said they were aware of the growing stakes, with the layoff notices going out next week. "I know there's a level of uncertainty with layoff notices going out. I think we all take that very seriously," Daudt said.

In recent days, Lt. Gov. Tina Smith has met privately with groups of workers at 10 of the affected agencies.

"For them it is not a political problem," Smith said. "It is a personal problem."

Staff writer Ricardo Lopez contributed to this report.

Patrick Condon • 651-925-5049