House Financial Services Committee Chairman Barney Frank (D-Mass.) on Thursday unveiled draft legislation that would expand dramatically the government’s role in stabilizing the shaky housing market.

The plan would rescue as many as 2 million people from foreclosure by allowing the Federal Housing Administration (FHA) to guarantee up to $300 billion in refinanced mortgages to distressed borrowers, according to a summary circulated by Frank’s staff.

“We hope to make this as least likely a loser for the government,” he said.

Frank also warned that there would be “concentric circles of victims” unless the government stepped in to stem the tide of foreclosures.

He and Dodd said they were working closely to move forward on legislation when lawmakers return in April after the Easter break. Dodd also circulated the key details of his proposal to reporters. The lawmakers indicated they would introduce separate bills, despite similarities in the drafts.

Under both plans, the banks and other institutions that service mortgages would opt in to the program voluntarily — and only after writing down mortgages so that they are more affordable to the borrowers. Mortgage servicers would have to find an FHA-approved lender to refinance their distressed loans.

“Lenders are going to have to take their losses,” Frank said, a pre-emptive strike at criticism that his plan would bail out banks and thereby encourage more risky lending.

Frank contends that his plan would cost very little, and could even make money for the government. However, the plan would expose the government to losses if the borrowers did not repay on the refinanced loans. It would also have a budgetary cost, in the form of a credit subsidy for the FHA guarantees.

The program would be temporary and the loans would be sequestered in a separate FHA fund to avoid imperiling the agency, which already backs mortgages for low-income borrowers.

Mortgages on vacation homes or homes bought for investment would not qualify. But Frank acknowledged that some reckless borrowers would benefit: “Some people who made imprudent decisions to buy homes will be helped by this.”

Both Dodd and Frank also gave minimal details on an alternative that would create an auction for mortgage holders to compete on writing down the loans.

The lawmakers have rejected bolder federal interventions that they and others have floated in recent weeks.

Frank has scaled back from having the government buying billions of dollars of mortgages and then reselling them to investors, an idea he appeared to be mulling until recently. Dodd has also abandoned a plan to create a separate federal entity, akin to the Depression-era Home Owners’ Loan Corporation, to buy distressed mortgages.

Frank said last week that the budget score for his proposal could be roughly $5 billion over five years, which would have to be offset under House pay-as-you-go budget rules. To avoid a painful hunt for offsets to comply with the rules, Frank said he is working with the Congressional Budget Office (CBO) to minimize the score.

“What the CBO score is will be a determinant of how much we can do,” he said.