A run of mishaps, including illness and the husband’s workplace injury, extensive structural damage from a burst water bed and the mother’s layoff from a nursing job, had already upended their middle-class lives. Then the pile of utility bills emerged as a headache to rival the past-due mortgage.

“You always try to pay your mortgage or rent to keep a roof over your head,” said Debra Cardente, the mother. “Then you ask, do you pay your electric or gas bill, pay your telephone or put food on the table?”

The recession has accentuated what was already a growing home-energy challenge for low-income and many middle-class households across the nation. Rising numbers have had their utilities shut off, causing desperate scrambles to pay arrears and penalties to get them restored.

In 2009, some 31,000 households in Rhode Island will have their utilities shut off, and the effort to juggle energy bills and mortgages is helping push some homeowners into foreclosure, said Henry Shelton, director of the George Wiley Center, a consumer advocacy group here. (Here, as in many states, utilities may not disconnect the poor in the winter.)

Since 2000, the cost of heating a home with fuel oil has more than doubled and the cost of heating a home with electricity has risen by one third, outpacing many incomes. The recent surge in unemployment has thrown even more people into energy debt.

Last winter, applications for federal energy assistance soared and Congress nearly doubled money for the program, known as Liheap, to $5.1 billion. In 2009, a record 8.1 million households, up from 6.1 million in 2008, received one-time grants, averaging about $500, according to data released Friday by the National Energy Assistance Directors’ Association.

Congress kept the financing at $5.1 billion for the coming year. Energy prices have dipped slightly, but applications this fall are up an additional 20 percent, so grants will shrink or more people will be turned down, the association said.

“Households will do just about anything to stay connected,” said John Howat, an analyst with the National Consumer Law Center in Boston. If they cannot pay, some people move and open a new account under a different name. Some run extension cords from a neighbor’s house, others spend weeks getting heat from dangerous kerosene stoves and light from candles.

The Cardentes got their power turned back on by borrowing money from relatives and paying $3,500 toward arrears of more than $10,000. But they defaulted on a plan that called for them to pay $723 each month, and the utility demanded the balance of almost $5,000. They are applying for Liheap aid and plan to appeal to the utility for more time.

For some low-income families, the federal grants have been welcome but just too small. Suzette Orazi, 50, and her husband, Juan Lizardo, 45, live with a teenage son in a house in Providence that is heated inefficiently with electric room units. As energy prices climbed over the last several years, so did their utility bills, while Mr. Lizardo lost his job as a jewel polisher.

The $1,000 they got from Liheap last winter hardly made a dent in their growing arrears, now over $11,000. The power company recently threatened to cut them off but later said that in accord with state protections for low-income customers, it would not do so in winter. It is still pressing for an immediate $2,456, however.

“We just can’t make that payment,” said Ms. Orazi, who receives disability. The couple fears losing the house as well as the electricity needed to live in it.

California, like Rhode Island, requires lower electric rates for low-income consumers. Even so, as unemployment in California climbed past 12 percent, the number of shutoffs among such families rose by one-fifth in the year that ended in August, according to a report last month by the state’s Division of Ratepayer Advocates.

In Connecticut, the number of shutoffs for all incomes rose from 86,074 in 2008 to 105,300 in just the first nine months of 2009, according to the state’s Public Utilities Commission.

New Jersey is widely praised for its program for low-income residents: a family of four making less than $38,588 pays only about 6 percent of its income on utilities. Those one step up, with incomes up to $49,612 for a family of four, are eligible for Liheap grants.

But many families just above that level, with incomes between $50,000 and $66,000, have found themselves in energy trouble in a high-cost state where unemployment is 9.7 percent. New Jersey Shares, a nonprofit organization that provides up to $1,000 in energy assistance to that group, has already helped a record 19,000 families this fall and turned away an additional 18,000 for lack of money, said its director, James M. Jacob. Many seeking aid are facing imminent shutoffs, he said.

With energy costs becoming a chronic challenge, consumer advocates in Rhode Island and elsewhere are pushing for alternatives to one-time grants, citing the program in New Jersey and a similar one adopted this year in Illinois, setting bills as a share of income.

Such an approach would make a world of difference for the Cardente family, for example; in hard times, their bills would have been cut, and when Ms. Cardente and her husband find work, the bills would rise.

New Hampshire already has income-linked subsidies, but in mid-December, citing rising hardship, the governor and legislative leaders said they would rush through a bill for still more aid. Indiana, Nevada, Ohio and Pennsylvania are among states that reduce utility bills according to income levels, said Mr. Howat, the consumer advocate.

The subsidies are usually paid for by raising rates for household, commercial and industrial customers, posing political risks. In Rhode Island, a bill to cap utility bills for the poor at 6 percent of income has been introduced by State Representative Arthur Handy, Democrat of Cranston. But in a statement last June, the state’s Division of Public Utilities and Carriers expressed “reservations” about the proposal, and its prospects remain uncertain.

James E. Lanni, the state’s associate administrator of utilities, said the plan would place an unreasonable burden on consumers, raising the average electric bill by 3.7 percent and the average gas bill by 5 percent to yield $15.2 million in subsidies. He said that the doubling of federal energy aid, along with other programs, had reduced need and that if fees were not linked to consumption, people would have no incentive to conserve energy.

In an interview, Mr. Handy countered that with his plan, utilities would save money on dealing with delinquent accounts and spend less money disconnecting and reconnecting homes.

The Rhode Island legislature is expected to consider the measure early next year.