Advocates for Miamians who live paycheck-to-paycheck are unveiling on Thursday an ambitious program to build as many as 1,000 new affordable housing units designed to prevent families from falling into homelessness. The program, which is being spearheaded by the Miami Coalition for the Homeless, aims to raise millions of dollars in private investment to encourage area developers to set aside units for “extremely low income” residents — renters who earn the minimum wage, or only about 30 percent of the city’s median income. Persuading developers to build such housing is enormously difficult without government or private subsidies.