A bipartisan pair of lawmakers have laid out the first substantial plan to redesign the nation’s mortgage market, nearly five years after the government spent more than $100 billion to rescue the system.

Sens. Bob Corker (R-Tenn.) and Mark Warner (D-Va.) introduced legislation Tuesday to replace mortgage finance giants Fannie Mae and Freddie Mac with a new government agency that would shift more of the risks of mortgage lending to the private sector.

“This bill has the opportunity to be the blueprint that could spark the debate both in the House and the Senate, and ultimately become” a pathway for reform, said David Stevens, chief executive of the Mortgage Bankers Association.

The senators are attempting to bridge the contentious divide in Washington over the role of the government in the housing market. Congressional Republicans, who partly blame Fannie and Freddie for the financial crisis, want to leave mortgage financing solely in the hands of the private market.

Many Democrats, however, argue that though the current system is not ideal, the government is needed to ensure that affordable mortgages are available for a wide range of Americans.

Since the financial crisis in 2008, Fannie, Freddie and other government-backed agencies have insured nearly 90 percent of new mortgages. While that has made home loans widely available despite the financial upheaval, it means taxpayers are at risk if homeowners default on their loans.

Against this backdrop, Corker and Warner have proposed a compromise that would make the government the last line of defense in the event of a housing crash. Under the new proposal, homeowners, banks and other private-sector firms would suffer first if a borrower stops paying a mortgage.

A borrower would either have to put 20 percent down to get a government-backed loan, or, if the borrower put down less money, would have to pay for mortgage insurance to make up the difference. That puts the borrower or private mortgage insurance company on the line for 20 percent of the value of the loan. (And the home could be sold for the remainder of the loan value, assuming that it has not declined in value by more than 20 percent.)

If the home’s value had dropped more than 20 percent — the bank issuing the loan would have to absorb losses, up to 10 percent of the value of the loan. Finally, if that’s still not enough, the government would promise to cover the losses on the loan.

The government would create a new single agency, modeled after the Federal Deposit Insurance Corp., to insure these mortgages. The new agency would charge premiums to lenders in exchange for the guarantee, which likely would be passed onto borrowers.

Most mortgage loans are pooled into securities that are traded around the world, from foreign central banks to domestic pensions. Without the U.S. government’s stamp of approval, investors would be more wary of putting money into American home loans, and financing the purchase of a home could become more expensive, as is it in many other countries.

Under Corker and Warner’s bill, Fannie and Freddie will have no more than five years to sell off their assets and cease operation. The Federal Housing Finance Agency would also be abolished and its staff and infrastructure transferred to the new government entity.

The legislation calls for banks to hold a piece of the mortgage-backed securities they sell to investors. While big banks have fought against rules requiring them to keep a stake in mortgages in the past, analyst suggest they could be swayed by being allowed greater access to the securitization process.

“A package that gives the bigger banks a broad role in packaging loans while ensuring community banks have unfettered access to mortgage securitizations is the best way to build industry support for legislation,” Jaret Seiberg, an analyst at Guggenheim Securities LLC’s Washington Research Group, wrote in a policy note.

But the way the government structures the loss and capital requirements could make it more difficult for borrowers to get a home loan. Lenders are sure to pass any additional costs they incur on to consumers. Capital requirements will likely be much greater for borrowers with low down payments and credit scores, which means those on the margins of the financial system could wind up paying more for a mortgage, Stevens said.

“Making sure that the first loss and private capital up front is substantial enough to protect the taxpayers, but not overly burdensome to the point where it restricts access to credit, is the dynamic tension we’ll be looking at in the coming weeks,” he said.

Despite calls by lawmakers and others to abolish Fannie and Freddie, the Obama administration has not offered any substantial plans to revamp the housing finance system since the government placed the firms in conservatorship in 2008. Rather, it has laid out options.

A White House spokesperson said Tuesday that the president “welcomes this bipartisan effort on reforming our housing finance system.” The administration wants to ensure that whatever system replaces Fannie and Freddie protects “the 30-year fixed-rate mortgage and broad and affordable access to housing for responsible working families from all communities,” the person said.

Getting the Corker-Warner bill through the House will be an uphill battle. House Financial Services Chairman Jeb Hensarling (R-Tex.) has been a strong proponent of fully privatizing the system.

“The GOP-controlled House is a real obstacle to reform even for measures that enjoy bipartisan support in the Senate,” Seiberg said. “One only has to look at the farm bill to see how more radical interests in the Republican Party can defeat a bill that emerged from the Senate on a bipartisan basis.”

There is a small chorus of investors who support restructuring, rather than eliminating, Fannie and Freddie. The tide of opinion started to turn some after Fannie May posted a record $7.6 billion in profits in the final quarter of 2012, making observers wonder whether they could survive without government support. Last month, Fannie Mae repaid the government $59.4 billion.

The overwhelming momentum, however, is behind doing away with the mortgage finance giants.