NEW HAVEN >> Jasmine Sullivan, a low-income mother of three, struggles every year to keep up with her heating bills and knows what it feels like to have her fuel source shut down for lack of payment.

For the past five years she has found the assistance provided with money from the federal Low-Income Home Energy Assistance Program helpful in the winter when her gas bill jumps to about $175 monthly, before it drops back to around $60 again in late spring.

She qualifies for some $535 out of the $585 maximum payment in LIHEAP funds, less than half of her annual gas costs. Sullivan, 30, also takes advantage of a matching payment plan offered by her utility to get a handle on clearing back bills.

“But, it’s always catch-up,” she said. She works part time, something she would increase if there was access to child-care options.

Sullivan is one of what Operation Fuel Inc. estimates are 313,000 Connecticut households who experience an affordability gap in covering energy costs even after LIHEAP distributes assistance to about 101,000 households in the state, said Patricia Wrice, executive director of Operation Fuel.

The LIHEAP website says Connecticut was awarded $72.3 million for fiscal 2016 and served some 103,000 households in fiscal 2014.

U.S. Sen. Chris Murphy, D-Conn., in a visit Monday to the Community Action Agency of New Haven on Whalley Avenue, said despite dropping oil prices, those savings are not being passed back to the consumer when it comes to heating oil deliveries.

Also, the number of residents who are financially strained by energy costs is increasing.

“We have more clients in need for longer periods of time,” said Amos Smith, president/CEO of CAA, one of the agencies in the state that takes applications and distributes LIHEAP funds to utilities for qualifying households.

Smith said people who lost good jobs in the 2008 recession may be working again, but they are not compensated at the same levels as before the recession.

“These are working class families who don’t get pay raises,” Smith said.

“Savings are evaporating and incomes are declining,” Murphy said.

Smith said CAA processes about 120 applications a day. This week they are slowing that down to catch up with a backlog. They estimate that they will have a 10 percent to 15 percent increase in applications this year; they have served some 13,000 households in Greater New Haven in other years from November to May.

Murphy said there is a fight between warm climate states and those like Connecticut that see temperatures plummet in winter.

With a snowstorm hitting the mid-Atlantic and Northeastern states hard this past weekend and another not far off, Murphy felt this was a good time to talk to people on the ground who see the need up-close.

“It’s not hyperbole to say this is a matter of life and death,” Murphy said when people can’t afford to heat their homes.

The senator said he was glad that LIHEAP was at least flat-funded instead of cut, although more is needed.

Murphy said he came to CAA to “experience firsthand,” stories on the need for more LIHEAP funds “to cure the cold-heartedness of some of my colleagues.” He said they feel the need is declining, “but that is not the case, especially in high-cost states.”

“If you are from Florida, you may not understand this,” Murphy said.

He said most of the recipients of the funds are working, but can’t make ends meet on minimum wage jobs.

Smith said they are projecting their applications will be up by about 10 percent to 15 percent this year. In past years they have helped some 13,000 households.

The LIHEAP award is keyed to those households which earn 60 percent of the gross state median income with the assistance ranging from $240 to $585.

This covers a household of 1 making $33,132; household of 2 persons earning $43,327; household of 3 earning $53,521 and a family of four earning $63,716.