A budget deal reached Friday between top legislative leaders hangs in the balance, as Gov. Mark Dayton is holding firm that any final budget should include funding for his top legislative priority of universal preschool.

Legislators are working through the weekend in hopes of ending the budget-setting session on time, but the last-minute warning by Dayton has heightened the prospect of a special session.

Monday at midnight is the constitutional deadline to adjourn and avoid a special session.

Senate Majority Leader Tom Bakk, DFL-Cook, and House Speaker Kurt Daudt, R-Crown, announced in a news conference at the governor's residence that they reached an agreement on key spending bills Friday. The deal struck would provide $400 million in new money for education, but Dayton is not satisfied by the boost.

"Either they refuse to fund E-12 education at [an additional] $550 million in the next fiscal year or they can come back in the special session to do so," Dayton said Friday.

Dayton said that he was in education funding discussions with Bakk and Daudt until about 4 p.m., when they asked to negotiate in private. Two hours later, there still wasn't a resolution, so he declined to join them when they met with reporters.

In addition to the larger funding boost for education, the governor also wants $173 million for half-day universal prekindergarten, according to deputy chief of staff Linden Zakula.

Dayton is expected to address reporters at 11 a.m. Saturday.

The fight over universal preschool has been brewing for months. On one hand, some early-ed supporters insist that boosting current preschool scholarships is more cost-effective because it targets low-income families and students that they say have the greatest need.

Dayton and his allies, including the statewide teachers union and House DFL legislators, argue that early-learning efforts need to be more comprehensive. He has proposed a modest expansion of existing scholarships and funding to eliminate the state's Head Start waiting list. Universal preschool's cost though is pegged at $394 million in his budget proposal. Fully implemented, it would cost close to $1 billion over two years and require more than 2,800 licensed teachers.

The Senate's education budget largely funding so-called school readiness programs, a move school boards support because they say they would struggle to pay for classroom space. Moreover, they say a shortage of licensed early-education teachers would make it difficult to meet the staffing requirements of Dayton's plan.

Photo: Gov. Mark Dayton speaks to a gathering of educators last month, urging them to push for universal preschool in the final weeks of session. (Jim Gehrz/Star Tribune)