Ed DeMarco, acting director of the Federal Housing Finance Agency, testifies Tuesday during a hearing before the House Financial Services Committee. (Jim Watson/AFP/Getty Images)

For more than four years, Fannie Mae and Freddie Mac have been a paradox of economic policy. Bailed out to the tune of more than $100 billion, the mortgage finance giants are widely despised — President Obama and congressional Republicans agree they should be abolished — yet they have played a critical role in the nation’s housing recovery.

Fannie and Freddie have been backing most loans, helping make sure low-cost mortgages are available to prospective home buyers. Without the companies, many analysts say, it is doubtful the mortgage market would have held up during the tumult of the past four years.

On Tuesday, the discussion about how to replace the companies — and design the nation’s housing finance system of the future — kicked up a notch in Congress, where sharp political divisions also made clear that finding a consensus about what to do next will be extraordinarily difficult.

Republicans and Democrats on the House Financial Services Committee agreed that it was time for them to draft legislation for replacing Fannie and Freddie. Yet their comments suggested a wide gulf on how they plan to do it.

The chairman of the panel, Rep. Jeb Hensarling (R-Tex.), suggested that he finds the companies culpable for the financial crisis in the first place and would be skeptical of any new plan that involves a significant role for government.

“After 41 / 2 years,” Hensarling said, “inaction is no longer an option, because [Fannie and Freddie] were at the epicenter of the financial crisis. They were part of a tragically misguided government policy to incentivize, browbeat and mandate financial institutions to loan money to individuals to buy homes they could not afford to keep.”

But the ranking Democrat on the committee, Rep. Maxine Waters (Calif.), suggested that the government still has a role to play in ensuring the housing market functions well for the majority of Americans.

“This committee should begin the job of considering the many bipartisan reform proposals on the table so that we can give the market certainty [and] guarantee the continued availability of the stable mortgage products like the 30-year, fixed-rate loan,” she said.

Many of the proposals focus on creating a federal entity that explicitly backs mortgages but makes sure that banks and lenders suffer first if homeowners cannot pay and charges high fees in exchange for the government insurance. Until they were bailed out in 2008, Fannie Mae and Freddie Mac had an implicit guarantee, prompting the companies to take excessive risks.

Ed DeMarco, acting director of the Federal Housing Finance Agency, the regulator of Fannie and Freddie, suggested that he would move on his own to remake both of them whether or not Congress or the Obama administration gets involved.

He is already creating a third company owned by both Fannie and Freddie that will house a number of joint functions. He is also increasing the fees they charge lenders and consumers for a mortgage guarantee, in hopes that private lenders will start competing to make loans that do not come with a federal guarantee.

The Obama administration has not weighed in recently on housing finance. In 2011 it released a white paper exploring different options for overhauling the system, but it has been quiet since. People familiar with the administration’s thinking say officials prefer maintaining a federal guarantee.