Gov. Mark Dayton is fighting to ensure that his signature priority — universal preschool — becomes part of a final budget agreement, issuing a veto threat Saturday and rallying Democratic allies in the House and the state party.

With less than two days left until the end of the legislative session, Dayton’s potential veto sets up what could become an expensive game of chicken. If the session goes into overtime, it would interrupt the schedule of the Capitol’s renovation, likely costing the state millions of dollars and leaving legislators scrambling for space to hold a special session, according to Senate Majority Leader Tom Bakk, DFL-Cook.

Further complicating the budget fight is the possible ­fallout should Dayton reject the education bill. Budget officials have warned that without an E-12 bill, the state Department of Education would shut down, schools would be forced to lay off teachers and applications for teacher licenses would go unprocessed, among other repercussions.

After days of negotiations at the governor’s residence, Bakk and House Speaker Kurt Daudt, R-Crown, on Friday night announced a budget deal that saw both men giving ground on their priorities: transportation funding for Senate DFLers and tax cuts for House Republicans.

On Saturday, Bakk said, “The speaker and I both gave up our number one priorities. Maybe [Dayton] has to give his up,” a reference to universal pre-K.

But Dayton is staging an all-out offensive in hopes of securing $173 million for a scaled-down version of his top goal, universal access to public preschool for all the state’s 4-year-olds. His latest offer is for a half-day, rather than all-day program.

Dayton also is demanding $150 million more than the $400 million for education that was agreed to Friday by legislative leaders.

“I’m going to veto $400 million because it’s wrong for the people of Minnesota, for the parents of Minnesota, and for the schoolchildren of Minnesota — it’s wrong,” Dayton told reporters on Saturday.

Legislative leaders are standing firm on their $400 million education budget, even though Bakk said he agreed with Dayton’s position on education. Bakk said he could not persuade House Republicans to accept it.

Daudt said, “I would be disappointed if the governor chose to veto $400 million, at least a 1.5 percent increase per year on the per-pupil formula, in new funding for Minnesota schools.”

Dayton allies, including House DFL legislators and the state DFL Party, Saturday began an end-of-session push for the governor’s universal preschool proposal.

“We have a unique opportunity to build on the progress we made together and make further investments in our kids and their schools,” said a House DFL letter sent at midday. “Unfortunately, the $400 million E-12 budget target announced yesterday is insufficient to make the kinds of investments that are needed.”

Talks among the House, Senate and governor’s staff continued late into Saturday night, including a meeting between Bakk and Dayton’s Chief of Staff Jaime Tincher.

Tensions were heightened when Minnesota Management and Budget Commissioner Myron Frans and Education Commissioner Brenda Cassellius issued a letter outlining the grim scenarios that could unfold if an education budget bill isn’t passed. Among other things, the state would be unable to process payments to schools, special ed and early learning funds would come to a halt, and state academies for the blind and deaf could be temporarily shuttered.

“The consequences of not enacting an E-12 education budget bill would be catastrophic for our schools, our teachers, and most importantly our students,” said the letter.

Saturday’s standoff comes after days of talks at the governor’s residence failed to produce agreement on taxes and transportation, two of the most contentious issues before the Legislature. Debate all session long has centered on how to handle the state’s projected $1.9 billion budget surplus. The current agreement between Daudt and Bakk leaves about $1.3 billion left that could go toward transportation spending and tax cut bills next year.

With spending targets in hand, conference committees are working through the weekend to finalize budget bills, with an expectation of finishing by the required adjournment of Monday at midnight.

Among the deals moving through the legislative process Saturday night was a compromise on how long law enforcement can retain data obtained through license plate readers. House and Senate members agreed on a 60-day window for retention of data. Lawmakers also agreed to provide additional funding for the state’s avian flu epidemic, setting aside $10 million for a loan program so farmers can replenish their flocks

The House also approved, 125-6, a measure that would ban four fire-retardant chemicals in household furniture and children’s products.

Legislators reached an agreement Saturday on the higher education bill, agreeing to give the University of Minnesota $53 million beyond its current allocation. Of that, $30 million will go toward the medical school to boost its national prominence. The Minnesota State Colleges and Universities System, meanwhile, received $101 million in new funding.

A compromise in the area of health and human services will give significant new money to nursing homes and preserve MinnesotaCare, a public health insurance program for the working poor.