State employees could start to receive layoff notices in the coming weeks if Minnesota lawmakers don't convene for a special session and pass a budget soon.

The state faces a partial government shutdown if legislators don't pass a new two-year budget before July 1. Layoff notices could go out before then since state employee contracts require at least 21 days' notice, and at least 30 days "whenever practicable."

"We have to send layoff notices to any entity that's not funded by June 1," House DFL Leader Melissa Hortman told reporters last week. "That is really the next deadline that comes after May 19, and human beings are deadline-driven."

Legislators had hoped to wrap up remaining budget bills and return for a special session this week so that agencies wouldn't have to send out the layoff notices. They've been working since their session adjourned on May 19 to finalize spending bills for health, human services, transportation, education and natural resources, among others.

"The progress that our committees are making at this point don't really leave any doubt in my mind that [a special session] will happen as soon as possible," House Speaker Lisa Demuth, R-Cold Spring, said late last week.

But that work has apparently slowed. On her way to a private meeting with Gov. Tim Walz and legislative leaders Tuesday afternoon, Hortman told reporters a special session "probably" won't happen until next week.

Much of the budget work is happening behind closed doors, so it's difficult to know precisely which policy disagreements are holding up the process and putting thousands of state jobs at risk.

The Legislature passed a handful of budget bills funding the Departments of Corrections, Public Safety and Agriculture before it adjourned, so those agencies wouldn't have to send out layoff notices.

Legislative leaders wanted to finish remaining budget bills by the Memorial Day weekend, but negotiations continued into Tuesday as legislators traded offers on a tax bill, debated a jobs and economic development package and discussed other bills in private.

Senate Majority Leader Erin Murphy, DFL-St. Paul, said last week that lawmakers were "making slow and steady progress."

"We are debating over things that we care deeply about and disagree strongly over, and people have to work through that," Murphy said.

While the actual debates are happening out of the public eye, lawmakers have said they are deeply divided over whether to roll back MinnesotaCare health coverage for undocumented immigrants. A budget deal struck by Walz and legislative leaders this month would end the coverage for undocumented adults while continuing it for children.

DFL and GOP leaders are debating whether the coverage repeal should be a standalone bill or included in the larger health budget. Many Democrats want to vote against the repeal without blocking the larger budget from passing.

Legislative leaders met with Walz for a check-in on Tuesday afternoon.

The governor told Minnesota Public Radio on Friday that he hoped to finish the budget before June 1.

"June 1 does matter because we are obligated by law with our contracts to send out those furlough notices, those layoff notices," Walz said.

"We have just a couple things to button up," the governor added.