First problem: the poverty line is variable. For one person under 65, it was ~$11k, for a family of two (single mom + kid, for instance) it's $15k, for a family of four it was $23k. Would you advocate a different minimum wage in each case? Or would you choose one? Those create, respectively, a $5.37, $7.27 and $11.08 minimum wage.
Second problem: at the minimum wage, you have to work every day of every week just to not be impoverished. There's no way to retire if you can never save, no way you can take an unpaid day (sick day, vacation day, personal day for your kid's doctor's appointment; I didn't have paid leave when I was a wage earner)... Heck, if your hours are reduced one week due to factors outside your control (your boss schedules your hours), you're in trouble. You're basically fighting every day just to tread water.