In December, however, the family’s housing nightmare ended with a proposal that at first seemed unreal. The Dobbinses’ lender, GMAC Mortgage, offered to erase a whopping $190,000 from their debilitating debt and cut the interest rate to 4.4 percent. That reduced the monthly mortgage payment to $1,400, almost half of what they were paying.

“I believed God was going to work things out for us and he did,” said Donald Dobbins, 45, a truck driver and father of three. “I’m ecstatic.”

The Dobbinses, who say they were victims of a high-interest predatory loan, join hundreds of homeowners in Massachusetts — and tens of thousands across the United States — who have received hefty home loan write-downs. Often, the discounts exceed $100,000.

The loan modifications are part of a federal government-driven campaign to help “underwater” borrowers — people who owe more than their homes are worth — and deal with the long-lingering foreclosure crisis.

Lenders, who have traditionally resisted wiping out mortgage debt, are now forgiving millions of dollars in loans, pushed by government incentives, political pressure, and a $25 billion settlement between five major lenders and 49 attorneys general.

GMAC Mortgage would not comment on the Dobbinses’ case, but said it is focused on helping borrowers struggling to pay mortgages.

“Principal forgiveness can be an effective tool to keep families in their home,” GMAC spokeswoman Susan Fitzpatrick said. Such efforts, she said, benefit “the borrower, the servicer, and the investors on whose behalf we service loans.”

But there is still disagreement among policy makers, economists, and housing advocates over the benefits of principal write-downs.

Edward J. DeMarco, acting director of the Federal Housing Finance Agency, which oversees mortgage giants Fannie Mae and Freddie Mac, prompted a political backlash in July when he rejected a US Treasury plan to give the taxpayer-controlled lenders money to fund write-downs.

In a letter to Congress, DeMarco allowed that up to 248,000 borrowers could be eligible for help, saving taxpayers as much as $500 million. Nonetheless, he turned down the plan saying it “would not make a meaningful improvement in reducing foreclosures in a cost effective way for taxpayers.”

Specifically, he warned of added administrative costs and the potential for “moral hazard,” meaning that by forgiving debt for some homeowners, the government might encourage others to default on their mortgages so they, too, could receive bailouts.

Instead, DeMarco said, mortgage companies should “strengthen” existing programs for troubled homeowners, such as refinancing and short sales — when properties are sold for less than the mortgage balance.

In August, Massachusetts Attorney General Martha Coakley called on DeMarco to change his position. Coakley doesn’t believe borrowers would purposefully stop paying their mortgages, and says stopping foreclosures is key to the nation’s economy.

“People don’t, by and large, default without a lot of agony,” she said.

Despite DeMarco’s stance, the number of principal write-downs is expected to swell as lenders work to meet guidelines of the national agreement reached in February between attorneys general and five major US banks over alleged foreclosure fraud and sloppy paperwork. The Treasury Department in February also tripled financial incentives for lenders to offer principal write-downs to homeowners as part of the federal Making Home Affordable program.

“There’s a very robust debate going on about the place that principal reduction can have in working out problems in the housing and mortgage market,’’ said Joe Smith, monitor of the North Carolina-based Office of Mortgage Settlement Oversight, which is overseeing the bank settlement. “The experience (in coming months) we have will help inform that discussion.”

The settlement with Bank of America Corp., JPMorgan Chase & Co., Wells Fargo & Co., Citibank, and Ally Financial Inc., owner of GMAC Mortgage, requires about $10 billion in principal write-downs over the next three years. Between March 1 and June 30, about 12,500 homeowners nationwide had loan debts cut, according to the oversight office. Another 28,000 were granted trial loan modifications with principal reductions, the report said.