President Barack Obama is proposing to overhaul the nation’s mortgage finance system, including shutting down government-backed Fannie Mae and Freddie Mac—a plan with bipartisan support on Capitol Hill. Obama will also insist that popular 30-year mortgages be widely available to borrowers, even in a system that would rely more on the private sector than the government to guarantee loans. The president was to outline his proposals Tuesday at a construction company in Phoenix, once the epicenter of the housing crisis following the 2008 economic collapse. The housing market in the region, as in much of the country, has rebounded in...