AUGUSTA, Maine — After working for weeks to fashion a compromise proposal that would address a shortfall in the Department of Health and Human Service budget, a deal remains elusive as a divide appears to be growing among lawmakers, especially House Republicans.

At the center of that divide is Gov. Paul LePage.

The governor has castigated lawmakers, first last week and then again this week, for failing to pass his budget and for crafting their own revised version that he said doesn’t address the problem.

On Monday, LePage directed criticism at the Appropriations Committee for tinkering with his initial proposal and for infusing a new, alternative proposal with “gimmicks.”

The governor went one step further and said that if the Legislature does not pass a budget with the structural changes to MaineCare he believes are necessary, he would veto what they do pass.

On Tuesday, LePage took yet another step and called on Republican lawmakers to stop working on a compromise with the Democrats and pass a simple majority budget.

“The governor believes the Democrats have been sitting on their hands,” LePage spokeswoman Adrienne Bennett said.

Over the last couple of days, the governor has met with Republican House and Senate members, presumably to gauge their support for his budget or the bipartisan alternative. On Tuesday, he met with members of the Legislature’s conservative caucus behind closed doors.

Republican and Democratic leaders already have been trying to sell the alternative budget proposal to their own caucuses.

Rep. Andre Cushing, assistant House majority leader, said he understands the governor is frustrated that the compromise bill contains things he doesn’t like. Cushing also said he respects the governor for reaching out to Republicans in the House and Senate.

“But I wish we were limiting it to the scope of the problem instead of taking swipes,” he said.

Asked whether he has support in his caucus, Cushing said he suspected some House Republicans would not vote for the budget, so the Democrats would be key to a two-thirds vote.

House and Senate Democrats remained hopeful of a bipartisan solution on Tuesday but their patience seemed to be waning in light of the governor’s continued criticism.

“This is a philosophical divide. It’s not a budget issue anymore,” said Jodi Quintero, spokeswoman for the House Democrats.

Instead of dealing with a $220 million shortfall for 2012 and 2013, lawmakers are addressing $140 million in MaineCare cuts to pay the state’s bills through June. That would be done by creating a hybrid budget bill that combines DHHS cuts with $25 million in savings identified by a streamlining task force.

Appropriations Committee members have agreed on some alternative savings initiatives, including: a proposal to better manage the use of opiate drugs for MaineCare patients, modifications and redesigns of some of the MaineCare optional services, a reduction and redesign of the developmental services waiver in MaineCare, and a rate reduction for services provided by methadone clinics.

Perhaps the biggest point of contention has been eliminating childless adults, or noncategoricals, from the MaineCare rolls. Democrats want to prevent the elimination of thousands of noncategoricals but have agreed in negotiations to a reduction in enrollment.

The governor indicated that piece was non-negotiable this week, saying he would veto any bill that didn’t include structural changes to eliminate coverage for noncategoricals.

Another piece that was stalling negotiations on Tuesday was setting the eligibility threshold for parents of children on MaineCare. It is now 200 percent of poverty level.

The governor wants to set the threshold at 100 percent. The Republicans in the House and Senate are leaning toward 133 percent, which would bring Maine in line with provisions of the federal Affordable Care Act. Democrats want to bring the line down only to 150 percent.

Late Monday night, LePage reportedly directed DHHS staff to stop working with the Appropriations Committee. His office would not confirm that but Republicans and Democrats on the committee did.

Bennett said the administration believes the Appropriations Committee “has all the information it needs.”

Since LePage rolled out his proposal to cut $220 million from the Department of Health and Human Service budget in 2012 and 2013, lawmakers have been working toward passing it with a two-thirds majority vote.

That means 101 votes in the Maine House or 24 votes in the Senate.

Both Republicans and Democrats in the Legislature agree that a two-thirds budget is crucial because the bill would go into effect immediately. A simple majority budget would not be enacted until 90 days after this session ends.

If the Legislature passes a two-thirds budget, it automatically has enough votes to override a veto from the governor. However, if the governor does veto, he would force the Republican-controlled Legislature to do something it hasn’t done since LePage took office: overturn one of his vetoes.

Cushing said the rhetoric from both sides is not helping the process and is not reassuring the public that lawmakers have their best interests in mind.

“We’ll make our case to our caucus,” he said, adding that there will be some who probably won’t get on board.

Negotiations were continuing late Tuesday.