Democrats and Republicans on Capitol Hill agree: Fannie Mae and Freddie Mac must go.

House Republicans passed a bill at the committee level Wednesday to wind down Fannie and Freddie in five years, and a bipartisan group on the Senate Banking Committee has introduced a bill that would do the same. But there is no agreement on what housing finance should look like after the two government-owned mortgage buyers are gone.

There's good reason for the disagreement: Freddie and Fannie, as private companies sponsored by the government, were always major players in U.S. housing finance. But since becoming government-owned entities in 2008, they have dominated the mortgage market.

Ed DeMarco, the top regulator in charge of Fannie and Freddie, warned in a March speech that the country "finds itself in the uncomfortable position of having over 90 percent of new mortgage originations supported by the federal government."

That level of involvement in home lending means that "they are the mortgage-backed securities market  Fannie and Freddie are basically it," said Federal Reserve Chairman Ben Bernanke.

The question facing lawmakers is whether, or to what extent, private companies can take over an industry that has effectively been nationalized since the collapse of the housing bubble in 2008. More specifically, the question is whether the defining feature of U.S. housing finance  the traditional 30-year fixed-rate mortgage  is viable without a government backstop.

The government did not end up controlling 90 percent of the secondary market for home loans overnight. Much of the federal government's role in housing markets began as part of the response to the Great Depression.

With the local banks and savings and loans that traditionally made three- to five-year home loans in crisis during the 1930s, the government took steps to create a more predictable, national market. In 1934, Congress created the Federal Housing Administration to insure mortgages against defaults. Four years later, Fannie Mae was founded to create a liquid secondary market for FHA-insured mortgages by buying them from lenders and selling them to investors. Knowing that Fannie would buy and securitize mortgages they made, home lenders made more home loans. Thanks to the early FHA and Fannie Mae, long-term, fixed-rate mortgages became a standard mortgage product.

Decades later, Fannie Mae transitioned from a government agency to a government-sponsored enterprise -- a government-chartered business with private shareholders. In 1970 Congress created a second GSE, Freddie Mac, to deepen the secondary market for mortgages. By the 1980s, the two companies began to resemble what they looked like before the 2008 crash: private companies with an implicit government backstop that tried to profit both by buying mortgages and by securitizing mortgages.

The rest is now history. In 2006, before the crash, Fannie and Freddie guaranteed 27 percent of all new mortgages (the GSEs guarantee loans they sell to investors, for a fee), according to Inside Mortgage Finance data reported by ProPublica. That was a relatively low share for the two GSEs, as private investors took over market share during the height of the housing frenzy. By the end of 2012, however, that share had risen to 69 percent.

Republicans now want to return to a pre-crisis state of affairs, but one without a quasi-governmental mortgage agency that risks another taxpayer bailout. The Republican bill that cleared the House Financial Services Committee Wednesday, the PATH Act, reflects a belief that the secondary mortgage market can function without any government backstops.

The PATH Act would create a privately run utility that would set standards for mortgage securitization, but it would not guarantee or purchase mortgage-backed securities. It would, however, promote affordable housing and expand housing credit during downturns through a slimmed-down FHA, which would continue to insure new mortgages. Otherwise, , the market would largely be privatized over time.

House Democrats, however, say the GOP plan would spell the end of the American housing market as we know it, and in particular lead to the end of the 30-year fixed-rate mortgage, by far the most common type of home loan-- which they consider an unacceptable outcome.

Maxine Waters of California, the ranking member on the House Financial Services Committee, said at a July 18 committee hearing that the GOP bill was a "radical and unworkable" plan and that it would "be bad for America's middle-class, ending the affordable 30-year fixed rate mortgage and making it a product only available to a tiny subset of lower-income FHA borrowers."

Adam Levitin, a Georgetown Law professor who testified at the July 18 hearing, said the 30-year fixed-rate mortgage is "a uniquely American and uniquely consumer-friendly product that furthers economic stability and monetary policy. The 30-year FRM is the crown jewel of the American housing finance system."

Thirty-year fixed-rate mortgages are much less common in Europe, where shorter, adjustable-rate mortgages are more the rule. Although all advanced nations provide some kind of government backstop for home lending, few make use of government-sponsored enterprises in the secondary market the way the U.S. has.

Levitin testified that the Republicans' bill would destroy the 30-year fixed-rate mortgage, arguing that there would be no market for long-term mortgage securities that are not guaranteed by the government.

Levitin distinguished between "credit risk" and "interest rate risk" investors. The former are willing to make bets based on the odds that a homeowner will fail to make payments on a home loan. Interest rate risk investors, on the other hand, only have the sophistication to make investments based on the outlook for interest rates, and are not capable of telling good home loans from bad ones. "The overwhelming majority of investors in the U.S. secondary mortgage market are not credit risk investors," Levitin said.

Without the loan guarantees provided by Fannie and Freddie, Democrats argue, investors in the U.S. market would be exposed to credit risk as well as to changes in interest rates. Many would leave, decreasing the liquidity of the secondary market for mortgages and thus making it harder for potential homebuyers to find financing for home loans.

The bipartisan Senate Banking Committee bill, co-sponsored by four Democratic senators, is designed to address concerns about liquidity in the secondary mortgage market by replacing the GSEs with a Federal Mortgage Insurance Corp., modeled after the Federal Deposit Insurance Corp. that guarantees consumers' bank deposits. The FMIC would be funded by premiums from participating companies and would provide insurance for mortgage-backed securities. The insurance would pay out only once private investors took a loss.

The purpose of the FMIC would be to assure interest risk investors that they would not be exposed to credit risk -- that they would not be on the hook for losses brought on by homeowners failing to make payments.

House Republicans do not believe that mechanism is necessary to support a housing market that includes a 30-year fixed rate loan. House Financial Services Committee Chairman Jeb Hensarling, R-Texas, said at a Tuesday mark-up of the PATH Act that "the 30-year fixed exists today without a government guarantee and the PATH Act won't change that." Republicans also have pointed to the existence of long-term mortgages available for houses too expensive to be insured by the GSEs or FHA as proof that a government backstop is not needed to maintain the 30-year fixed rate mortgage.

Hensarling may be able to win support for his bill among House Republicans, but conservatives do not expect that Senate Democrats or the White House will be convinced anytime soon that their plan would not upend U.S. housing finance.