More budget talks were expected Thursday as Minnesota’s legislative session hurtled toward a midnight Sunday deadline with no deal on a $3 billion deficit.

The Democratic-controlled Legislature defied another veto threat from Republican Gov. Tim Pawlenty late Wednesday and sent him a health and welfare package he opposes. Democrats hope to make a key provision — an expansion of Medicaid health care for poor adults — part of a deal.

The health bill was pushed through with just enough time for Democrats to try to override a veto if Pawlenty takes the maximum three days to reject the bill. At least three House Republicans would have to join all the chamber’s Democrats to overturn a veto — a prospect that appears unlikely. No House Republicans voted for it and five House Democrats voted against it.

Lawmakers who weren’t part of budget negotiations waited for the shape of a final agreement to appear. The legislative session can run until Monday, but the state constitution doesn’t allow lawmakers to pass bills on the last day. That means the practical deadline is Sunday.

“It’s kind of like a bad movie. I’m waiting to see who the villain is after all these subplots get through,” said Sen. Don Betzold, a Democrat from Fridley.

Top GOP lawmakers were upbeat after Wednesday’s negotiations. They have been pressing Democrats to make some of last year’s budget cuts permanent and use the savings to pay back schools for delayed state aid.

“I think there’s a positive solution,” House Minority Leader Kurt Zellers, R-Maple Grove, said.

But Senate Majority Leader Larry Pogemiller, a Minneapolis Democrat, called the idea a “storyline.” He said there’s no money to pay back schools. The state is projected to face a deficit of at least $5.5 billion in the upcoming two-year budget period.

“If you designate something that you’ve already cut as paying back something that you can’t pay back, I don’t think that really accomplishes anything,” Pogemiller said.

The budget crisis is more severe after the state Supreme Court undid Pawlenty’s 2009 budget fix last week because of the way he imposed it. He delayed payments to schools and temporarily cut spending on a number of programs.