AUGUSTA — Maine lawmakers enter the homestretch of the legislative session this week, and budget negotiators are speeding up efforts to resolve major partisan disagreements, most notably the voter-approved 3 percent tax surcharge on wealthy Mainers.

Key legislators plan to meet Sunday to begin trying to close the divide before time runs out.

The new fiscal year is still six weeks away, but lawmakers have less than a month to pass a roughly $7 billion two-year state budget in order to give themselves time to respond to a potential veto from Gov. Paul LePage.

LePage vetoed the last two-year budget in 2015. And it is clear that the Legislature’s end product this year will again look significantly different from LePage’s $6.8 billion budget proposal, which included tax cuts, the elimination of 500 state employee positions and a major overhaul of the state’s K-12 funding system.

Republicans and Democrats would need two-thirds votes in the House and Senate to override a LePage veto.

Yet Democrats and Republicans remain at odds on the biggest issue affecting the budget: whether to preserve or eliminate the 3 percent tax surcharge on earnings above $200,000 that voters approved last November. The ballot question was intended to funnel more state money into public schools and bring the state’s contribution up to 55 percent of education costs, a level that was mandated by voters but never achieved.

“It is incredibly important to Democrats that we meet the obligation to get to 55 percent,” Rep. Drew Gattine, D-Westbrook, said. “Democrats have a very clear idea about how that should be paid for and the way to do that is the 3 percent surcharge. . . . Republicans keep talking about wanting to get out from under the 3 percent surcharge, but they have yet to come up with a plan to do that.”

NOTHING IS OFF THE TABLE

Republican lawmakers and Gov. LePage have been adamant about eliminating the surcharge because they say it would drive away high earners and hurt the economy.

House Minority Leader Kenneth Fredette, R-Newport, said the two sides “have been in a stalemate now for a pretty long time” over the bigger issues. He had a succinct response when asked if House Republicans saw room for compromise with Democrats on the 3 percent.

“No,” Fredette replied. “The reality is this is just really simple, basic economics. We don’t want to be the highest-taxed state in New England. We are certainly competing with our New England counterparts.”

At the same time, both sides say that nothing is “off the table” as they try to reach a compromise on the two-year spending plan. And while the word “shutdown” has come up occasionally among lawmakers in recent weeks, legislative leaders and members of the budget-writing Appropriations and Financial Affairs Committee aren’t using it.

“I think reasonable heads are going to prevail and we will get where we need to be,” Fredette said. “It is going to be a tough lift.”

Gattine, the House chairman of the appropriations committee, said he also is confident the two sides will find common ground in time to pass a budget. But on the 3 percent issue, he again emphasized that the Republicans need to come up with an alternative plan to increase funding for education.

Cross-party discussions are happening elsewhere at the State House as well.

On Friday, LePage met privately with House Speaker Sara Gideon, D-Freeport, and Senate Minority Leader Troy Jackson, D-Allagash, to talk about education. The 3 percent tax hike, which LePage fiercely opposed, was reportedly part of that conversation.

It’s not unusual for the Legislature to go down to the wire on budget negotiations before the two parties begin to compromise.

The Maine Constitution requires a balanced budget to continue operations, so budgets needs to be passed every two years by July 1 or the state government shuts down. That hasn’t happened since 1991, when Maine’s state government shut down for more than two weeks after budget negotiations got mired in a political showdown over workers’ compensation.

NEGOTIATIONS BEHIND CLOSED DOORS

Two years ago, the word “shutdown” loomed as a late budget deal between Democrats and Senate Republicans ran into a wall of opposition from House Republicans backing LePage’s position that any budget needed to include tax cuts. The final budget did include tax cuts but LePage still vetoed the spending plan, forcing lawmakers to return to Augusta to override his veto hours before state government was due to shut down.

By this point in the legislative session, much of the appropriations committee budget negotiations occur behind closed doors, making it hard to monitor for the media and other interested parties, including LePage, who often accuses lawmakers of striking “secretive backroom deals.” Two years ago, legislative leaders effectively took over negotiations from the committee after the first deal fell apart amid an interparty split between House and Senate Republicans.

On Friday, the Republican and Democratic leaders of the appropriations committee met privately to discuss the path forward.

“We have effectively established everyone’s viewpoints,” Sen. James Hamper, R-Oxford, the committee’s co-chairman, said with a smile when asked how the discussions were going. “Did it get us to a resolution? No.”

Those discussions will continue Sunday.