Poverty level for a 4-person household (which a single mother with three children would be) is $22,050/year. 3-person is $18,310.
50 hours a week @ $7.25/hr (federal minimum wage) * 52 weeks/year = $18824.
Although, good luck finding 50 hours a week of work in this economy.
And that only applies to US citizens. Never mind undocumented immigrants. (Though many do earn minimum wage and pay taxes.) Restaurants will often split low-income workers to avoid either restaurant giving them more than 40 hours a week, so they can avoid overtime and benefits.