More than 2 million families now use Section 8 vouchers to keep from becoming homeless. It's the government's largest program to help low-income families pay their rent. Usually, the tenant pays up to 30 percent of their income in rent and a local public housing agency makes up the difference.

But Congress had bigger plans when it created the nearly $20 billion program in the 1970s. The voucher was designed to be a ticket out of poverty– allowing families to use it wherever they want. With a portable voucher, families can move to places with jobs, good schools and low crime.

So far, however, the program has not always lived up to that promise, especially when it comes to women with children. Among voucher holders, a 2016 government study found fewer than 13 percent of female-headed households with children were able to move to areas with higher opportunity.

Section 8 housing proposals face stiff opposition in cities across the US, including the McKinney and Frisco suburbs of Dallas, Texas. An opponent, Nicole Humphrey, owner of ShutterView Photography in Frisco, proclaimed, "In this neighborhood, most of us are stay-at-home moms with young kids. The lifestyle that goes with Section 8 is usually working, single moms or people who are struggling to keep their heads above water. It's just not people who are the same class as us."

Read More | Nicole Humphrey, 'Not Racist or Bigot,' on Class and Section 8 Housing