The Senate banking committee’s top leaders on Tuesday released the broad outlines of a plan that would dismantle mortgage giants Fannie Mae and Freddie Mac, advancing what many observers expect will be a multi-year effort to revamp the nation’s housing finance system.

For months, Sens. Tim Johnson (D-S.D.) and Mike Crapo (R-Idaho) have worked to hammer out a plan they could agree on and sell to their respective parties. In a joint statement, the lawmakers said they would unveil their legislation in “the coming days.”

But the bill is expected to face many hurdles, in part because leaders of both parties are not eager to take on a complex and politically fraught issue in the lead-up to this year’s midterm elections.

The legislation builds on a plan by Sens. Bob Corker (R-Tenn.) and Mark R. Warner (D-Va.) that would replace Fannie and Freddie with a new entity — the Federal Mortgage Insurance Corp. — and shift more of the risks of mortgage lending to the private sector.

District-based Fannie and McLean-based Freddie do not make loans. They buy them from lenders, package them as securities and sell them to investors. They also insure mortgages, paying the investors should the loans go bad. The companies, which were seized by the federal government in 2008, were widely blamed with exacerbating the financial crisis by buying millions of risky loans and passing on the risk to consumers.

The market always assumed that the government would step in if the companies faced extraordinary losses, and it did, giving the institutions $188 billion in bailout money.

Like the Corker-Warner plan, the Johnson-Crapo initiative would have private capital cover the first 10 percent of losses on mortgage-backed securities, even though the mortgage industry had lobbied for a lower threshold. The new plan also would create an insurance fund, paid for by fees from the issuers of the securities, that would protect taxpayers against future bailouts.

“There is near unanimous agreement that our current housing finance system is not sustainable in the long term and reform is necessary,” Johnson, the Senate banking committee’s chairman, said in a statement Tuesday.

Some House Republicans immediately criticized the plan for keeping the government involved in the housing finance system, albeit in a more limited role. But the White House was equally quick to support the initiative, calling it a “good-faith compromise.”

“Both sides made difficult concessions in order to move this debate forward,” Bobby Whithorne, a White House spokesman, said in a statement. “We support this effort and believe it is a workable bipartisan approach to complete the biggest remaining piece of post-Recession financial reform.”

The plan calls for underwriting standards that would mandate a 5 percent down payment from borrowers, though it would carve out an exception for first-time home buyers, who would have to put 3.5 percent down.

It also eliminates the affordable-housing goals at Fannie and Freddie and instead sets aside a fund paid for by industry fees that would go toward ensuring the availability of affordable housing, the statement said.

Housing finance experts who have been tracking the issue say that simply having the two top leaders of the Senate banking committee come to agreement on this topic is significant in that it gives the Senate a starting point for debate on the issue.

But not this year, not even if there is broad support for getting rid of Fannie and Freddie, said Brian Gardner, a senior vice president at Keefe, Bruyette & Woods.

“I’m skeptical that the majority leader wants to put vulnerable Democrats in the awkward position of taking tough votes on the housing finance system,” Gardner said.

Even if the Senate moved swiftly, the House would not, said Guy Cecala, publisher of Inside Mortgage Finance, who predicted the bill would be dead on arrival.

On the House side, Rep. Jeb Hensarling (R-Tex.) has offered legislation that would get rid of Fannie and Freddie and strip the government of any role in the housing finance system. That legislation also is not moving, but it is telling of the mind-set among that chamber’s Republican majority, Cecala said.

Besides, with Fannie and Freddie reaping huge profits these days, it’s hard to make a case to shake up the status quo, Cecala added.

The Office of Management and Budget estimated this week that the two companies would send $180 billion in profits to the U.S. Treasury during the next 10 years.