The Fed says that unemployment will remain high for years.
Some Republican congressmen are trying to take away the goal of ensuring full employment from the Fed. See this and this.
Conservatives argue that the relationship between inflation and unemployment - as represented in the Phillips Curve - is false, and therefore the rationale behind the dual mandate makes no sense. See this, this and this.
Liberals like economist James, Galbraith, congressmen Jerry Nadler and Alan Grayson and Senator Bernie Sanders are defending the Fed's mandate to maximize employment.
But I think that all of their arguments pro or anti the Fed's dual mandate are missing the point.
Specifically, the Fed's dual mandate was created more than 30 years ago, in 1978.
The Fed has had this full employment mandate all throughout this economic crisis. But it is indisputable that the Fed's actions have been increasing unemployment. See this and this. Indeed, John Williams puts the current real unemployment rate at around 23%.
The Fed had the mandate in 2007, 2008, 2009 and 2010 ... but it acted to save the big banks instead of the American worker.
And yet the Fed has been given more and more power - even though it has been increasing unemployment ... and even though the American people already thought the Fed had too much power. See this, this and this.
So the problem isn't the Fed's dual mandate ... the problem is that the Fed has too much power. And the Fed has wielded that power to save its shareholders (the big banks), at the expense of Main Street and the real economy.