AUGUSTA — Lawmakers on the budget writing committee missed a self-imposed deadline Monday to complete work on the state’s next two-year spending plan in the face of a deep and potentially disruptive rift between Republican leaders in the House and Senate.

Members of the Appropriations and Financial Affairs Committee had hoped to finalize work on the $6.57 billion budget by Monday to give themselves enough time to get the measure through the full Legislature and override a threatened veto from Republican Gov. Paul LePage. But House Republicans were resisting a tentative deal struck late Sunday night between Republican leaders in the Senate and the Legislature’s Democratic leadership because the package does not contain income tax cuts or welfare reforms sought by LePage.

The two sides didn’t appear to be much closer to an agreement Monday night. The four House Republican members of the Appropriations Committee voted against several budget items in non-binding votes, but were outnumbered by the seven Democrats and two Senate Republicans.

One of those items added $50 million in funding for K-12 education that Democrats hailed as “a huge victory” and House Republicans said is either increasing state spending or diverting funds from other programs.

“How can we be supportive of that?” said House Minority Leader Rep. Kenneth Fredette, a Newport Republican leading the opposition to the proposed compromise between Democrats and Senate Republicans.

The divide imperils not only the passage of the tentative deal, but also the continued operations of state government if a new budget is not in place when the fiscal year begins July 1.

At issue are a number of initiatives proposed by LePage in January, including a massive overhaul of the state’s tax system, an income tax reduction and changes to the General Assistance program. All of those proposals have been rejected in the tentative agreement, which was negotiated by Senate President Mike Thibodeau, R-Winterport, and House Speaker Mark Eves, D-North Berwick.

On Monday, Thibodeau urged members of his party to support the budget plan, because it includes a provision that will make it harder for future legislatures to raise the income tax.

The provision is a constitutional amendment that, if ratified by voters, would require future income tax increases to receive two-thirds support from the House and Senate. A similar proposal, which has been a Republican goal for years, was among reforms that were narrowly defeated in the Legislature in 2005.

Thibodeau said the provision was a “historic opportunity” to curtail future spending while holding the line on income tax increases. The budget deal doesn’t include an income tax cut because lawmakers were unable to resolve key differences between the LePage administration and Democrats, who control the House of Representatives. The governor had proposed reducing the income tax and paying for the cut by increasing the sales tax and expanding it to currently exempt goods and services.

Thibodeau said that he and Republicans could not support that plan, in part because many in his party had helped overturn a similar tax overhaul passed by Democrats in 2009. The tax overhaul was revoked by a Republican-led ballot initiative in 2010.

“I ran against expanding sales tax in 2010,” Thibodeau said. “Maine people spoke loudly. We can bring sales tax down now.”

As part of the budget deal, a temporary sales tax increase that raised the rate from 5 percent to 5.5 percent will expire June 30. The agreement also includes eliminating income tax on pensions for military retirees.

Thibodeau and Senate Majority Leader Garrett Mason, R-Lisbon Falls, stressed those provisions Monday, saying that the plan managed to extract major concessions from Democrats.

“Nobody in a divided government gets everything they want, people recognize that and expect us to work together,” Thibodeau said. “It’s like Sen. Mason said, ‘This isn’t Burger King, we can’t have it our way.’”

However, the deal’s failure to include an income tax cut or to change the funding formula for General Assistance has put Thibodeau at odds with LePage and Fredette. The division, underscored when Thibodeau and Fredette held separate news conferences with State House reporters Monday, raises the possibility of a government shutdown.

The Maine Constitution requires a balanced budget to fund the operations of state government. Funding for nonessential services expires at the close of the current fiscal year, June 30. Appropriations Committee members had hoped to have a final agreement by Monday in order to allow staff in the Office of the Revisor of Statutes to draft the language of the bill – which is hundreds of pages long – and give lawmakers time to consider the bill before the Legislature’s adjournment on June 17. LePage then has 10 days not including Sundays to either sign the bill, veto it or allow it to become law without his signature. To override a veto, lawmakers would need two-thirds majorities in both chambers – a feat that would not be possible in the House if Republican members hold ranks and vote with LePage.

The budget committee is expected to continue working to close the budget on Tuesday. It already has taken a number of non-binding votes on a number of items, including rejecting major changes to the way the state reimburses municipalities for General Assistance. Those changes likely would have cost Portland millions of dollars and are part of a larger battle between the city and the LePage administration over welfare for immigrants.

During hours of negotiations – nearly all of it done behind closed doors – Democrats and Republicans on the Legislature’s budget-writing committee made progress on key issues related to education funding, social services, municipal “revenue sharing” and property tax exemptions.

Committee members rejected LePage proposals to increase the sales tax from 5.5 percent to 6.5 percent and administration plans to eliminate a host of tax exemptions for goods and services, such as haircuts, legal services and peanut butter.

The governor’s sales tax increase and base-broadening proposal were designed to help the government pay for income tax cuts, which LePage has cast as the centerpiece of his $6.57 billion two-year budget proposal and a major focus of his second term in office.