This sounds kind of like the earned income tax credit, which is basically a reverse tax (if you don't make enough to pay taxes, you get a subsidy instead): http://en.wikipedia.org/wiki/Earned_income_tax_credit

Expanding EITC substantially would be politically easier than attempting to do this, since it already exists and has bipartisan support (as opposed to raising the minimum wage). You need some sort of job for the EITC, though.