President Obama will appear at a Falls Church community center Wednesday to unveil a plan to ease the sluggish housing market by making it easier for homeowners to refinance their mortgages.

President Obama. (Charles Dharapak/AP)

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Up to 3.5 million people who do not currently have federally backed loans might be eligible for the program, administration officials said, and another 11 million people who currently hold government-backed loans from Fannie Mae and Freddie Mac could potentially benefit. The president will offer details at 11 a.m. at the James Lee Community Center in Falls Church.

The move, first reported by the Wall Street Journal, comes amid a rapidly growing consensus that the nation’s moribund housing market is holding back the economic recovery. Home values are hovering at eight-year lows, and more than 10 million people are underwater, or owe more than their homes are worth.

The Obama administration has tried several different strategies to pump life into the market, including another refinancing plan that the president outlined last fall in Las Vegas, the foreclosure capital of the nation.

Under the plan Obama will announce Wednesday, borrowers would be eligible if they have a minimum credit score of 580 and a loan that falls within the Federal Housing Administration’s limits, which range from $271,050 to $729,750.

The government also is willing to pay closing costs for those who agree to use their savings to pay down the principal of their mortgages, rather than reducing their monthly payments, the administration official said.

The plan’s estimated price tag is between $5 billion and $10 billion, and the administration proposed to pay for it through a tax on large banks that Republicans have opposed.

With his appearance in Falls Church, Obama is returning to Virginia for the third time in the past six months, hoping to rally support for his reelection in an important battleground state. In 2008, Obama became the first Democrat to win the state in a presidential election in 44 years.

His campaign recently added staff and plans to open a fourth Virginia office this weekend.