Credit ratings agency Fitch Ratings projects that about two-thirds of borrowers with permanent modifications under the Obama plan will default again within a year after getting their loans modified.

Obama administration officials contend that borrowers are still getting help — even if they fail to qualify. The administration published statistics showing that nearly half of borrowers who fell out of the program as of April received an alternative loan modification from their lender. About 7 percent fell into foreclosure.

Another option is a short sale — one in which banks agree to let borrowers sell their homes for less than they owe on their mortgage.

A short sale results in a less severe hit to a borrower’s credit score, and is better for communities because homes are less likely to be vandalized or fall into disrepair. To encourage more of those sales, the Obama administration is giving $3,000 for moving expenses to homeowners who complete such a sale or agree to turn over the deed of the property to the lender.

Administration officials said their work on several fronts has helped stabilize the housing market. Besides the foreclosure-prevention plan, they cited government efforts to provide money for home loans, push down mortgage rates and provide a federal tax credit for buyers.

“There’s no question that today’s housing market is in significantly better shape than anyone predicted 18 months ago,” said Shaun Donovan, President Barack Obama’s housing secretary.

The mortgage modification plan was announced with great fanfare a month after Obama took office.

It is designed to lower borrowers’ monthly payments — reducing their mortgage rates to as low as 2 percent for five years and extending loan terms to as long as 40 years. Borrowers who complete the program are saving a median of $514 a month. Mortgage companies get taxpayer incentives to reduce borrowers’ monthly payments.

Consumer advocates had high hopes for Obama’s program when it began. But they have since grown disenchanted.

“The foreclosure-prevention program has had minimal impact,” said John Taylor, chief executive of the National Community Reinvestment Coalition, a consumer group. “It’s sad that they didn’t put the same amount of resources into helping families avoid foreclosure as they did helping banks.”