ALBANY — New York lawmakers and Gov. Andrew M. Cuomo said a state budget they expect to start voting on Thursday will include lower taxes on households earning $300,000 or less, and a phased $15 minimum wage. A legislative source also said school aid is expected to increase by $2 billion.

By late Wednesday night, the major sticking points had tentative agreement, according to two legislative sources briefed on the tentative agreement, although some final details were being worked on overnight.

Late Wednesday night, the Assembly tentatively signed off on the proposal to raise the minimum wage to $15 in phases over six years, which has been the most contentious element of the budget, a state source said. The Assembly had agreed to the last revisions by the Senate, which will require review of the minimum wage after three years to make sure it isn’t costing jobs or acting as a drag on the economy, the source said.

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The deal, and others in the $154 billion budget, will have to be finalized, printed, debated and passed by midnight Thursday if the budget is to be on time before the start of the fiscal year. But several legislators were doubtful that could happen, which would take away a point of pride for Cuomo and legislators this legislative election year.

“We’re proceeding down the path that minimum wage is still in the budget,” Assembly Speaker Carl Heastie (D-Bronx) said hours earlier.

Cuomo and Heastie confirmed the tentative agreement on a tax break first proposed by the Senate’s Republican majority.

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The governor said he and legislative leaders have agreed to a “framework” of a tax cut that likely will be included in a roughly $155 billion state budget. The tax plan, as floated, would create several new tax brackets at the lower and middle end of the pay scale. Those couples earning the maximum eligible for the break, $300,000, could see their tax rate lowered from 6.57 percent to 6 percent.

That would closely follow a tax-cut proposal that Senate Republicans advanced earlier this year.

“We’re OK with it, it’s really more of a Senate request, but we’re OK with it,” Heastie said.

Cuomo and legislative leaders were also contemplating an increase in school aid of more than $2 billion and are expected to rescind a recession-era measure called the Gap Elimination Adjustment that has taken a slice of school aid increases each year, according to a state source briefed on the latest closed-door discussions.

“We have a deal in place that will finally do away with the GEA and undo the damage done when our state wrongly took much-needed revenue away from our schools,” said Assmb. Todd Kaminsky (D-Long Beach).

The school aid increase under discussion would be more than the 4 percent — or $991 million — increase proposed by Cuomo in January, which would have raised school aid to more than $24 billion. The highest counterproposal has been a $2.1 billion increase over current funding pushed by the Assembly’s Democratic majority.

Senate Majority Leader John Flanagan (R-East Northport) has promised a “record” increase in school aid. Cuomo has said the school aid increase in the budget under negotiations would be “very positive from every point of view.”

The Assembly’s Democratic majority also appeared to have won on a top priority Wednesday.

Heastie said after a series of closed-door negotiations and meetings with his members that one of the biggest sticking points that delayed talks has been tentatively resolved. Heastie had insisted on eliminating Cuomo’s proposal to shift $250 million in Medicaid costs back to New York City.

“It is off the table,” Heastie said Wednesday.

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That’s also a big win for Mayor Bill de Blasio, who has lobbied hard to overturn the proposal by Cuomo, who has feuded with the mayor.

“The governor said this would not cost New Yorkers one penny more,” said de Blasio spokeswoman Amy Spitalnick. “We took him at his word and expect him to keep his word.”

Heastie said his Democratic majority is open to a “collaborative” process among the state, New York City and counties statewide to reduce Medicaid costs, which are now paid solely by the state. Cuomo argued the current system creates little incentive for local governments to cut fraud and waste. Heastie said the tentative deal will mean one municipality isn’t “picked on.”

“Medicaid was big,” Heastie said, striking a far more optimistic tone about the closed-door negotiations. “The fact that that’s better means we are in a better position.”

Heastie also said a measure to provide paid family leave for workers is also expected to be part of talks that picked up late Wednesday afternoon.