Both sides of the government have frequently expressed a desire to reform the GSEs, which now play an outsized role in the mortgage market. The agencies back more than 80% of the new mortgages originated today and guarantee more than 60% of the overall mortgage market. That puts taxpayer money at risk.

However, there is considerable disagreement on what the future housing finance system should look like. Some on the right believe the government should completely exit the mortgage market and that the presence of any kind of guarantee, even if explicit, will make the system unstable.

Others believe that there should be some kind of government backstop, but that the guarantee should be made explicit, so that taxpayers are at least compensated for the risk.

Under the new legislation, Fannie Mae and Freddie Mac will be replaced by a new government agency called the Federal Mortgage Insurance Corporation. The agency will collect premiums from the industry. In the event of a crisis, the FMIC will act as a backstop, stepping in to insure investors from losses but only after private capital has absorbed 10% of the security losses.

"When you've got a 10 percent capital buffer in advance it really causes that pricing of risk to be far less important because what you have out there is a huge investment by the private sector in advance of any kind of government reinsurance and that ought to be soothing to taxpayers," Corker said at the news conference, according to Bloomberg.

The bill also removes the affordable housing goals of the GSEs and instead establishes a Market Access Fund that will collect fees to maintain access to housing, provide grants to state housing agencies and conduct borrower counseling program.

This should curry some favor with conservatives as well.

Still, analysts believe the bill would struggle to pass in the Republican-controlled House, where conservatives are expected to argue for a completely private housing finance system.The Senate Banking Committee also has expressed a desire to reform the Federal Housing Administration first.

And others are also working on alternate proposals to restructure Fannie Mae and Freddie Mac.

Which means, the debate is likely to continue and shareholders may be stuck in limbo for a while.

-- Written by Shanthi Bharatwaj New York.

>Contact by Email.

Disclosure: TheStreet's editorial policy prohibits staff editors and reporters from holding positions in any individual stocks.

If you liked this article you might like

Mortgage Payments Could Be Hurt by Harvey's Impact on Houston

Fannie Mae: 36,583 Homes it Covers are in Harvey's Path

Fannie Mae and Freddie Mac Would Be Privatized Under Proposed House Budget

RBS Agrees to $5.5 Billion Fine in Pre-Crisis Mortgage Probe