There’s an interesting article on the effectiveness of housing vouchers at the Center on Budget and Policy Priorities you might be interested in. Here’s a snippet:
Rigorous research shows that vouchers — which enable families to rent decent, modest, private-market housing for about 30 percent of their income — sharply reduce the frequency with which low-income families move and the share of such families that live in overcrowded housing, doubled up with other families, in shelters, or on the streets (see chart).
That’s the sort of policy that should be able to garner bipartisan support.
Those benefits disappear if the father stays in the picture as that’s not what the Obama administration defines as “family’.