AUGUSTA — “Welfare” has become one of the most divisive words in Augusta. But lawmakers say that addressing the so-called welfare “cliff” may be one area where they can find common ground this year.

Legislators on both sides of the aisle agree that one of the biggest problems with the welfare system is that it can discourage recipients who want to work from taking a job or accepting a raise because they lose all their benefits once they reach a certain income threshold.

Because that threshold is well below the poverty level, people who earn just enough money to get kicked off may face an even bigger struggle to pay their bills than when they were on the program, lawmakers say.

“It’s almost like there’s a penalty for people that work,” said Rep. Drew Gattine, a Democrat from Westbrook and House chairman of the Health and Human Services Committee, who has introduced legislation aimed at alleviating the problem.

Republicans who are also pushing measures this session designed to make the transition from welfare to work easier say they’re eager to work with Democrats on the issue. But the “devil is in the details,” said Sen. Eric Brakey, who leads the Health and Human Services Committee with Gattine.

“There has been a lot of talk about it, but nailing down specifics on how we achieve that … is not something that has been figured out,” the Republican from Auburn said.

Currently, a parent with two children on the Temporary Assistance for Needy Families program loses benefits once he or she starts making more than $1,023 a month. If a recipient starts earning just more than that, he or she would still be unable to support a family but could no longer get assistance, advocates for the poor say.

Gattine wants to get rid of that income threshold for current recipients and ensure that for two months after recipients begin working, their earned income won’t be counted against them and their benefits aren’t immediately reduced. The Democrat is also proposing changes to the benefit calculation formula that would increase payments to the working poor.

Brakey and House Republican Leader Ken Fredette want the state to consider the creation of what they call a “tiered welfare” system, which would allow benefits to be lowered gradually as someone’s income rises. Brakey’s bill is a concept draft, which means the details would be worked out in committee in collaboration with the Department of Health and Human Services, he said.

A similar measure that would have created a group to study ways to fix the welfare cliff was never funded by Democratic leaders after passing both chambers. Democratic House Speaker Mark Eves’ office says there were many studies that needed funding and that was not on its priority list.

Fredette, a Republican from Newport, said he doesn’t believe it should be a partisan issue.

“This is about giving people the opportunity to have the dignity of having a job without facing the tough decision” of whether they will lose all of their benefits, Fredette said. “If Democrats want to come to the table and have meaningful conversations about the issues … Republicans are there and want to work with Democrats,” he said.

Republican Gov. Paul LePage has talked frequently of the need to create a tiered welfare system, including in his most recent inaugural address, but has never introduced measure to do so. A spokeswoman for LePage said he’s interested in the issue but that details of proposals he plans to introduce this session are not yet available.

While measures regarding welfare have been the source of contentious debates at the State House in the past, advocates say they believe this issue provides an opportunity for the two parties to come together.

“I think it enjoys broad bipartisan support (because) I think it makes so much sense,” said Chris Hastedt, public policy director for Maine Equal Justice Partners, which is behind Gattine’s bill. “I’m hopeful we will be able to come to some sort of agreement on this stuff.”