Starting Thursday, Connecticut residents can apply for help paying their heating bills. But politicians are squabbling over how much assistance to offer this winter.

With heating oil prices still at record highs, many homeowners could get "hosed." And this year, they may get less help from the state, thanks to federal relief money that's drying up. Now, Republican leaders want lawmakers to return to Hartford for a special session.

"We hear constantly from our residents, they are worried about how they are going to heat their homes," said state Rep. Vin Candelora (R-North Branford), the Connecticut House Minority Leader.

GOP lawmakers want to put more state money into Connecticut's Low-Income Home Energy Assistance Program. Their proposal would shift $120 million in American Rescue Plan funds from the Connecticut Department of Economic Development to LIHEAP.

"What we're proposing is easy," said state Sen. Kevin Kelly (R-Stratford), the state Senate GOP leader. "It's what the legislature does. It comes into session and does good things to help people in need."

Families could see a 40% drop in assistance. Last winter, the most vulnerable households qualified for $1,015, but this year, it's just $600. On Monday, three legislative committees approved reduced benefits based on less federal funding. The amounts could change if more federal money comes in.

On Wednesday, Gov. Ned Lamont said he wants to wait and see if Congress acts, especially when President Joe Biden is seeking more funding.

"I think it's just premature," Lamont said. "If the winter is bad and the feds don't step up, I've got a [legislative] session that starts in January. We'll be able to address that."

Kelly accused Democrats of waiting for Washington to "bail them out." His House counterpart shot back at Lamont.

"He needs to stop running around with his press conferences, doling out money -- what he thinks Connecticut needs, and actually give them what they actually need," said Candelora.

Democratic leaders in the state Senate called the GOP proposal a "political game Republicans frequently play," but also signaled they would consider a special session – after the November election.

"In addition, we will need to make a decision prior to Dec. 1 on whether to continue the gasoline tax suspension and the suspension of bus fares," Senate President Martin Looney (D-New Haven) and Senate Majority Leader Bob Duff (D-Norwalk) said in a joint statement. "Those and other issues which may present themselves may be addressed after the election in an atmosphere of governing rather than that of a political campaign."