I take it you are self-employed? Anyone who is on payroll making 10k a year gets earned income tax credit, so they would only be contributing the 6% employee share to SS, and indirectly the 6% employer share (through getting lower pay than the employer is willing to pay). Those are then completely offset by the earned income tax credit.
Yeah, I’m self-employed. I work for myself and I teach. Single, no deductions, etc. So I don’t qualify for any of the Obama benefits, but I sure as heck pay for them.