The chairman of the Senate Banking Committee and his Republican counterpart announced Tuesday that they had reached an agreement to dissolve bailed-out government-sponsored mortgage enterprises Fannie Mae and Freddie Mac and reform federal housing finance policy.

Sens. Tim Johnson, D-S.D., and Mike Crapo, R-Idaho, said in a joint press release that they would release legislative text in coming days that would closely mirror an existing bill sponsored by a bipartisan group of senators on the committee, led by Sens. Mark Warner, D-Va., and Bob Corker, R-Tenn.

Both bills would wind down and eliminate the mortgage behemoths Fannie Mae and Freddie Mac, which were taken into federal conservatorship after failing in 2008 and have remained in the government's control since. In recent months, the two companies have returned to profitability, so far yielding the government more in dividends than the $187.5 billion it cost to bail them out.

Both Senate measures would establish a Federal Mortgage Insurance Corporation, modeled on the Federal Deposit Insurance Corporation that provides depositors' insurance for banks. The FMIC would provide insurance on approved mortgage-backed securities that would only kick in once the private owners of those securities had suffered some losses. The FMIC would be intended to ensure a liquid market for mortgage securities while avoiding taxpayer losses on guaranteed loans.

The Johnson-Crapo plan would eliminate federal housing affordability goals in favor of housing funds taken from FMIC user fees and provide a securitization platform that would allow for standardized mortgage securities without Fannie and Freddie's influence.

Fannie and Freddie do not issue loans but buy mortgages from lenders and package them into guaranteed securities to sell to investors. In recent years, following the collapse of the housing bubble, Fannie- and Freddie-backed mortgages have accounted for as much as two-thirds of all new home loans.

The details of the differences between the Johnson-Crapo plan and the Warner-Corker plan are not yet known, but it was widely expected that, as chairman and ranking member, the two senators would want to put their own stamps on the legislation that would likely prove to be at the center of congressional debate in the years ahead. Although the political atmosphere is thought to preclude action on housing finance reform during the current Congress, lobbyists and housing activists have suggested that the bipartisan Senate bill will likely be the vehicle for reform in the medium-term.

Originally, Johnson and Crapo had said that they hoped to introduce their own measure in 2013. But the drama surrounding the government shutdown and the debt ceiling interrupted their schedule.

Although it is not actively involved in the push for housing finance reform, the White House has signaled support for the basic outline of the Senate bipartisan bill. President Obama said last year that the Corker-Warner principles were "consistent" with his own.

But House Republicans are not on the same page. The House Financial Services Committee, led by Chairman Jeb Hensarling of Texas, last year approved a bill to wind down Fannie and Freddie and remove the government's involvement in backstopping mortgage-backed securities. Instead, that legislation involved a privately run utility that would have standardized mortgage products without involving a guarantee. The federal government would retain a role in subsidizing mortgages only through the Federal Housing Administration, which insures loans for low-income home buyers. The House Republican bill would relax the FHA’s requirements during a downturn, to allow it to play a countercyclical role.

That bill, which is opposed by homebuilders' groups, has not advanced in the House, nor does it have support in the Senate.

Hensarling issued a statement Tuesday in which he thanked Johnson and Crapo for working to end the "unacceptable" status quo. But he also said that he is "skeptical" of any plan that does not end government guarantees in secondary mortgage market, warning that the bill could "perpetuate the cycle of boom, bust and bailout we tragically just witnessed."