AUGUSTA, Maine — A legislative committee charged with striking a budget deal this week continued its efforts to work toward a compromise Wednesday, a day after Democrats put forward a number of ideas to raise new revenue and Republicans didn’t bite.

Amid that work, a range of groups tried to insert their voices into the Appropriations Committee’s debate surrounding Maine’s two-year state budget, trying to take advantage of the apparent impasse.

A group of conservative Republican lawmakers outlined their plan for making $136 million in budget cuts and raising $230 million in new revenues to partially offset deep cuts to municipal revenue sharing and property tax relief programs proposed in Gov. Paul LePage’s budget.

Meanwhile, a coalition of Maine mayors said competing Democratic and Republican proposals that partially restore revenue sharing and other property tax relief measures don’t go far enough. Members of the state employees union picketed for a restoration of merit- and longevity-based raises. And the state’s main teachers union called for temporarily hiking Maine’s 5 percent sales tax to 6 percent to raise additional funds for public schools.

“I hope that … they will come forward with their own revenue proposals,” Rep. Peggy Rotundo of Lewiston, the appropriations panel’s Democratic House chairwoman, said of Republicans. “We both keep working toward each other, and we eventually meet and, what’s fair is when we meet halfway between where we both started, and that’s what we’re looking to achieve.”

On Tuesday, Republican committee members put forward a plan to restore about 35 percent of the revenue sharing funds cut under LePage’s budget proposal, increase funding for the homestead exemption that exempts the first $10,000 of residents’ property value from taxes, and offer property tax relief for low-income residents through an income tax credit.

Democrats countered with an offer to restore about three quarters of the revenue sharing funds cut under LePage’s proposal and largely maintain funding for the homestead exemption and circuit breaker property tax relief programs. Committee negotiations stalled when the discussion turned to how to pay for it.

While Democrats pulled back their previous proposal to put off implementing $400 million in income tax cuts for two years, they offered plans to raise Maine’s 5 percent sales tax to 6 percent temporarily, hike Maine’s $2-a-pack cigarette tax to $3.50, raise taxes on other tobacco products, and boost the 7 percent meals and lodging taxes to 9 percent.

Republicans said they had no appetite to consider new revenue sources until more budget cuts are made.

“I’m sure we’re going to come to a solution as we have to,” Rep. Kathleen Chase of Wells, the Appropriations Committee’s ranking Republican, said Wednesday. “Our concern is that we really have to have made all the adjustments we can possibly do before we even look at the revenue piece.”

Rep. Aaron Frey of Bangor, a Democrat on the committee, said Republicans haven’t given majority Democrats an indication of where in the budget they want to see cuts and to what degree.

“We have to come up with some number [in cuts], and I don’t even know what that is, before they will even engage in a conversation on whether they will consider revenue,” Frey said. “By implication, they’re considering revenue because their plan that was laid out last night was about $150 million, and it’s not clear where that money would come from if it’s not from revenue.”

In terms of cuts, Chase said Republicans are interested in scaling back some Democratic proposals that restore cuts proposed in LePage’s budget to programs such as municipal revenue sharing and the Drugs for the Elderly program in the Department of Health and Human Services, which provides prescription drug assistance to seniors.

“While they might not be full cuts,” she said, “we feel as though there’s a really good indication [Democrats] could come down from where their position is.”

Ultimately, “it really is the majority’s responsibility to come forward with something we can adopt,” said Rep. Dennis Keschl, R-Belgrade, another Appropriations Committee member.

The conservative Republican lawmakers who weighed in on the budget proposal offered a slate of cuts to programs including the Efficiency Maine Trust, the University of Maine System, Maine Public Broadcasting, the state Office of Information Technology and Medicaid coverage for transportation to drug addiction treatments involving methadone.

The group proposed raising $150 million from nonprofit organizations with more than $250,000 in assets — such as hospitals — calling it a “recycling fee” for receiving state funds for their programs. The proposal also would have the state take $82 million from the Maine Health Access Foundation, which the Legislature formed in 2000 after the sale of Blue Cross Blue Shield of Maine to Anthem. That transaction generated $82 million for the foundation’s endowment.

The 14 Republicans pitched their proposal as a way to slim down state government operations without raising taxes.

Increasing taxes “just makes it more difficult to remove ourselves from this tax-and-spend vortex,” said Rep. Heather Sirocki, R-Scarborough.

The 14 Republicans included the Republican leader in the Senate, Sen. Michael Thibodeau of Winterport, but Republican leaders in the House distanced themselves from the effort.

“There are different people who have different ideas on how to balance the budget,” said House Republican Leader Kenneth Fredette of Newport. “They represent themselves and themselves only.”