House Republicans on Thursday released the details of legislation that would shutter mortgage finance giants Fannie Mae and Freddie Mac and nearly eliminate the government’s role in backing the nation’s mortgage market.

The measure, which is expected to be introduced this month, could also limit the number of moderate-income families and others who get their mortgages from the Federal Housing Administration.

GOP lawmakers, who partly blame Fannie and Freddie for the financial crisis, have long wanted to shut down the companies and leave the mortgage-lending business to private actors.

But Democrats and some moderate Republican senators say that could limit homeownership, and they question whether the private sector would issue mortgages without a government backstop.

In contrast to the House bill, the Senate introduced a bipartisan measure that would replace the mortgage giants with a new government agency that would act as the last line of defense in a housing crash.

The senators’ push to keep the government involved in the mortgage market may be the sticking point that stymies a bill from passing in both chambers.

Over the past five years, Fannie, Freddie and other government-backed agencies have made home loans widely available by insuring nearly 90 percent of new mortgages. But their actions have placed taxpayers at risk if homeowners default on their loans and have made the mortgage industry heavily reliant on the federal government.

House Financial Services Committee Chairman Jeb Hensarling (R-Tex.) said the House bill aims to eliminate those risks.

“Our plan helps taxpayers and homeowners. It gives power and control back to consumers,” he said. “Under the current broken system, unaccountable Washington elites have more of a say over who gets a mortgage than your local bank.”

But some analysts feel it would close off homebuying to many Americans, especially those with lower credit scores.

“Underwriting criteria would be tighter, which means fewer consumers could qualify for mortgages,” Jaret Seiberg, an analyst at Guggenheim Securities’ Washington Research Group, wrote in a policy note.

The House Republican bill would preserve the FHA, the agency that provides mortgages more cheaply than the private sector for qualified borrowers, many of them first-time homebuyers. The FHA suffered considerable losses after the housing crash that put the agency at risk of exhausting its reserves.

But the legislation would restrict wealthier borrowers from tapping FHA loans and force the agency to halve the amount of insurance coverage it offers to lenders when loans fail. The bill would also raise down-payment requirements for the FHA from 3.5 percent to 5 percent for borrowers who are not first-time buyers.

“I am strongly disappointed in the Chairman’s legislation, which is little more than an attempt to reinvent America’s housing finance system using the same kind of right-wing ideology that has eroded America’s middle class for decades,” Rep. Maxine Waters (Calif.), the ranking Democrat of the finance committee, said in a statement. The congresswoman said Hensarling sought no input from the Democrats, unlike his colleagues in the Senate.

There is little chance of Hensarling’s bill getting through the Democrat-led Senate or even garnering broad support from the housing lobby, analysts say. If nothing else, the bill would advance discussions on Capitol Hill about how to redesign the nation’s mortgage market.

Despite the momentum in Washington to eliminate Fannie and Freddie, a small chorus of investors support restructuring the two. The tide of opinion started to turn after Fannie and Freddie returned to profitability last year, making observers wonder whether they could survive without government support.

Fannie and Freddie’s future has been widely debated since the government placed them in conservatorship in 2008 during the worst of the housing crash. The government purchased $188 billion worth of shares in Fannie and Freddie to keep them afloat. As they have returned to profitability, they have given the Treasury $132 billion in dividend payments to date.

Investors are mounting a fight to get the government to release its hold on Fannie and Freddie. This week, hedge fund Perry Capital filed a lawsuit in federal court to stop the government from seizing most of the profits at the firms. A similar class-action suit was filed Wednesday by another group of investors.