Bangor, Maine ? The low point in Kimberly Henderson’s struggle to keep her family warm came in early January when she was too broke to order an oil delivery and had to buy a 5-gallon container to take to her dealer to get enough fuel to make it through the night.

But later that month, with the gauge on her 275-gallon tank again approaching empty, Henderson’s fortunes turned around when she got a phone call from a local clergyman: He just received a donation that would provide her with 50 gallons of heating fuel that day.

“I could have cried,” said Henderson, a 40-year-old single mother of three who lives in a rental home in downtown Bangor. Like many in Maine, she has been hit hard by heating oil prices that have soared to an all-time high of $3.35 a gallon, or roughly $1 more than a year ago.

While many get help from the federal Low Income Home Energy Assistance Program, the average LIHEAP benefit of $750 isn’t enough to fill the standard oil tank at today’s prices.

That’s why volunteer efforts like the Rev. Gerald Oleson’s Sunny Corner Fuel Assistance have sprung up to help those who fall through the cracks.

Maine, where four out of five households heat with oil, is making an unprecedented push to raise private money this winter to help the tens of thousands who walk a financial tightrope in order to balance heating expenses with the costs of other necessities like food and medicine.

Stepped-up efforts are also under way elsewhere in New England. The nonprofit Massachusetts Energy Consumers Alliance, which draws from public and private sources, expects to extend $320,000 in assistance this winter through its Oil Bank program. That’s up from $128,000 last winter. Central Vermont Public Service Co., the state’s largest utility, has enlisted businesses to join in its heating assistance program.

In Maine, donations have ranged from $250,000 from outdoors outfitter L.L. Bean in Freeport to an anonymous fifth-grader’s gift of her $5 weekly allowance. Best-selling author Stephen King, who lives in Bangor and is known for his generous support of community fundraising efforts, has made an unspecified contribution to the local community action agency’s fuel assistance program.

The state also has its Operation Keep ME Warm, an initiative started five years ago that seeks private donations to help poor people pay fuel bills.

While Keep ME Warm brought in between $25,000 and $50,000 in past years, this winter’s total has already exceeded $1 million.

“The need is very acute this year and there’s a real sensitivity to what’s happening,” said John Kerry, who heads the state energy office.