WASHINGTON — More than five years after the government seized control of Fannie Mae and Freddie Mac, a Senate panel plans to take a major step Tuesday toward ending the mortgage giants’ state of limbo.

The Senate Banking Committee will consider a measure that would wind down the companies during a five-year period and shift most of the risk of mortgage lending to the private sector, an effort often cast as the last major overhaul to tackle after the 2008 financial crisis.

It may be days before the committee votes on the bill, which is expected to pass barring any last-minute surprises. Most of the panel’s 22 members — six Democrats and six Republicans — have signed on. Committee Chairman Tim Johnson, D-S.D., and Sen. Mike Crapo of Idaho, the panel’s most senior Republican, are the lead sponsors.

The suspense surrounds the final vote count. The more committee members who support the bill, the more likely it is that Senate Majority Leader Harry Reid, D-Nev., will bring it to the floor for a full vote. Supporters are eager for quick action to build on bipartisan consensus while Democrats remain in control of the Senate and President Obama remains in the White House.

“This might be the only real chance we have this decade to achieve reform,” Housing and Urban Development Secretary Shaun Donovan said at a recent event hosted by the Bipartisan Policy Center.

But there are challenges ahead. Although a wide range of coalitions support the idea of revamping the housing finance system, they don’t all agree on the means.

One potential stumbling block is the future of the 30-year, fixed-rate mortgage. The staunchest Republican opposition to the Johnson-Crapo measure comes from lawmakers who want to dramatically limit or end the government’s backing of mortgages in order to avoid a repeat of the $188 billion taxpayer-funded bailout of Fannie and Freddie in 2008.

Johnson-Crapo is built around the premise that the government’s backing is critical to preserving the 30-year, fixed-rate mortgage — a mainstay of homeownership in the United States.

While Fannie and Freddie were like other publicly traded companies before the crisis, the market assumed that the government would step in if there were extraordinary losses, and it did. The legislation takes that implicit government guarantee and makes it explicit.

Why? Because it’s the rare institution that wants to invest in mortgages for a 30-year stretch without some assurance that the government would step in to cover catastrophic losses, said Mark Zandi, chief economist at Moody’s Analytics. In most of the world, where governments do not back mortgages, the 30-year, fixed-rate loan is tough to find.

But the Johnson-Crapo bill seeks to limit taxpayer exposure by having private capital absorb the first 10 percent of losses on mortgage-backed securities. That money would have to be exhausted before the government would cover additional losses.

Fannie and Freddie buy mortgages from lenders, package them into securities and sell them to investors. For a fee, they insure mortgages and pay investors should the loans go bad.

Under the new system, private firms or “guarantors” would take on the insurance role. They’re the ones that must set aside 10 percent capital and take a hit before taxpayers. In other words, they must be able to remain solvent if 10 percent of the mortgages they insure default.

But the legislation is vague on what kind of capital would count toward the 10 percent requirement, and each type of capital has a different cost. Whatever the costs, they would be passed along to borrowers in the form of higher interest rates.