But in August, the Massachusetts Legislature rejected the plan, saying in part that cheap energy would flood the market and thwart attempts to advance wind and solar projects. That halted the whole effort.

“The impasse just kicks the can down the road, and I see no reason why this dynamic isn’t going to be repeated during the heating season for years to come,” said John Howat, a senior policy analyst at the National Consumer Law Center, a Boston-based nonprofit advocacy group for low-income residents.

“I think we need to be more aggressive in pursuing renewables and energy efficiency,” Mr. Howat said. “But I doubt we can implement those solutions quickly enough and at a sufficient scale to relieve the economic burden in the short term on those 30 percent of households that don’t have sufficient income to pay these bills.”

The problem may be getting worse, not only because of pipeline constraints but because old coal and oil power plants are being retired. The Vermont Yankee nuclear plant, which supplies nearly one-third of Vermont’s electricity, is also scheduled to go offline this month.

ISO New England, the independent system operator that oversees the region’s energy market, said it expected there to be “sufficient resources” this winter to meet demand. But in a November assessment, it called the pipeline constraints severe and said the reliability of the system would “continue to be threatened” until the region expanded its pipeline capacity or invested in other energy sources.

Figuring out how much new pipeline might be enough is not an easy calculation. Massachusetts, for one, is analyzing its needs now for a report due at the end of the month. It is a complex process, said Mark Sylvia, the state’s undersecretary for energy, because it must take into account the state’s desires to avoid dependence on one type of fuel, reduce greenhouse gas emissions and ensure reliability “so the lights stay on.”