WASHINGTON — In another sign that the housing market has strengthened, President Obama on Tuesday will outline his long-awaited ideas for overhauling the mortgage finance giants Fannie Mae and Freddie Mac to significantly reduce the government’s risk in any future credit crisis.

In an appearance in Phoenix, Mr. Obama will endorse bipartisan efforts in the Senate to wind down the two companies and end their longtime implicit guarantee of a federal government bailout. That dread prospect, once thought improbable, was realized in the fall 2008 financial crisis; Fannie Mae and Freddie Mac, then bankrupt, were made conservators of the government at great cost to taxpayers, who only now are being repaid.