As far as I know the Humphrey-Hawkins Full Employment Act of 1978 is still the law of the land, but has never been implemented in any strong way because the executive branch put it out to pasture. Carter, then Reagan, etc..
But if it is still on the books it offers an interesting possibility.
It isn't new law.
So here is the question for the wonkish... could this work:
President Obama reverses all executive orders and findings that prevented H-H from ever resulting in action. He then makes a supplemental budget request to congress for $150 billion to implement provisions in H-H. The request is a reconciliation-eligible budgetary item to fund existing law, not a whole new policy. So only 50%+1 required for passage. (Like all those Bush mid-year war-funding requests.)
Under H-H, as passed in 1978, the executive branch is empowered (arguably mandated, but I digress) to directly create (FDR-style) as many low-wage jobs as necessary to reach 3% unemployment. (The act specifies that jobs be created at the low end first, which is sound economics. You don't want people quitting existing jobs so the H-H jobs are presumed to be a measure to put a floor under the labor market. Most importantly, the concept is to soak up low-skill urban unemployment. Urban unemployment is currently about 17%.)
No filibuster. Not a vast sum of money... smaller than what we have come to view as a typical budget supplemental. And under H-H the executive can craft the programs with a surprisingly free hand.
$150 billion should easily cover a year of minimum wage make-work for 4-6 million people. That eliminates deflationary wage pressure in most urban areas and cuts national unemployment some. I doubt all those slots would be filled... the idea is to soak up all possible demand for those jobs. Nobody has to take them. They are an option added to the economy. These would not be good jobs, but they would force private minimum-wage employers to compete. McDonalds would go back to minimum wage +$2, as was typical in tight labor markets in the '90s. Cashier jobs in nice stores in the city go to McDonalds+$2, and so on.
And even folks who are not eligible for unemployment benefits can always easily put a few extra dollars in their pocket, which is better than the alternative. Teenagers. Elderly on fixed incomes. Homeless.
Politically, sell it as a measure that ensures that any able-bodied person willing to work can work, albeit for small wages. The public loves the idea of poor folks working (versus asking for a hand-out... you know the language.)