Representative Michele Bachmann promises to “turn out the lights” at the federal Education Department. Gov. Rick Perry calls it unconstitutional. Newt Gingrich, the former House speaker, would allow it to live but only as a drastically shrunken agency that mainly gathers statistics.

Even Mitt Romney, who in 2008 ran for president defending No Child Left Behind, the federal law that vastly expanded Washington’s role in public schools, now says, “We need to get the federal government out of education.”

For a generation, there has been loose bipartisan agreement in Washington that the federal government has a necessary role to play in the nation’s 13,600 school districts, primarily by using money to compel states to raise standards.

But the field of Republican presidential candidates has promised to unwind this legacy, arguing that education responsibilities should devolve to states and local districts, which will do a better job than Washington.