As you say, the neoliberal "corporate reformers" privatization program IS the current education policy of Obama admin and Democratic party. From what I've read so far, Chicago is where they started the program and are proceeding to make it national.
So no matter how we would like to frame it, this is in reality a political strike against Democratic administrations whole corporatocratic education policy. So should Obama and Democrats support the people who are striking against their education policy? Errr... of course they should change their policy, duh. We don't want their neoliberal shite no more, we loath it. If politics of the street and grass roots movements are strong enough to pressure out 90 degree change of the policies of the establishment, good. If they are too stupid and stubborn to yield and serve the people instead of corporations, what Clint said: get rid of them.