Under the administration's plan, "banks and other financial institutions will be required to hold more capital to withstand future recessions or significant declines in home prices and adhere to more conservative underwriting standards," the report said.

The government should require increased guarantee fee pricing and larger down payments, the report added.

Fannie and Freddie were private companies that were backed by the government, but because of mounting losses, the government placed them into conservatorship in September 2008.

According to the Treasury Department, 90% of mortgage loans that were made last year were guaranteed by a federal government program.

The report outlines three policy options: reducing the government's role in insuring and guaranteeing mortgages; keeping the government as a backstop credit source during difficult economic times; and offering government insurance for certain mortgage-backed securities.

But in a speech that he gave on the day the report was issued, Treasury Secretary Tim Geithner said that the administration believes it would be "fundamentally untenable for the country to adopt a model where the government plays no role."

Congressional Republicans are firmly in the camp of getting the government out of the mortgage market as quickly as feasible.

"What we need is legislation that protects taxpayers from further losses and future bailouts and builds a stable housing finance system based on private capital," House Financial Services Committee Chairman Spencer Bacchus (R-Ala.) said in a statement.

But Rep. Barney Frank (D-Mass.), the panel's top Democrat, said that while there need to be changes in the housing finance system, it is "not clear whether private markets by themselves will provide enough capital to make reasonably priced mortgages available to families that can afford them."

Officials at CUNA and NAFCU said that given credit unions' unique structure, they would be hurt more than other financial institutions if the secondary mortgage market weren't available.

CUNA Executive Vice President and General Counsel Eric Richard, a former associate general counsel of Freddie Mac, said that because of economies of scale, privatization is a "recipe for giving a lot of business to the big banks."

NAFCU Vice President and General Counsel Carrie Hunt noted that "credit unions have excellent loan quality but don't have the volume that others have so they might be hurt."

She added that because credit unions can't raise outside capital, they have to rely on the secondary market to raise money to help them make more mortgages and must strike a balance between serving members and keeping a diverse portfolio.