Getting the Federal Government out of civilian education is important far beyond what it would save in Federal expenditure. It is a step towards the uniformity that the Left seeks, for openers.
Education is inherently a local affair--between teacher & student. The Feds get into it, to satisfy the Egalitarian/Collectivist mentality, which wants everything uniform; that wants to make sure that a more successful community does not give its children the natural advantage that they would otherwise, quite properly, expect. It also allows those such as Obama, who hate traditional American culture, to throw impediments into our passing on traditional culture--and the specific local nuances of traditional culture.
It also, manifestly, creates an expense burden on State & local institutions--and draws teachers out of the class-room into the bureaucracy, as States ramp up their departments to interact with the Federal, and the communities ramp up their departments to interact with both the increased State & Federal bureaucracies. The whole thing is akin to a "keystone cops" absurdity.
You want a robust education system, with base minimum standards for mathematics, composition, and creativity development. Don't throw the baby out with the bath water just because the current system is terrible -- we can reduce the budget while reducing the mission to the very core that made the DoE a desirable thing to institute in the first place. The DoE was founded because there was a need for it at the time. We had so many damned agencies involved at the federal level with education that we streamlined it in the late 70s with one cabinet-level post. The constitutionality of that notwithstanding (That wily commerce clause just lets us to anything! apparently), we even expanded it under Bush II. If you were to kill the DoE, as Reagan wanted, you will have to face off in the courts against lawsuits claiming persons with disabilities will be impacted, people of color, and endless lawsuits that will just wrack havoc on the unity of this country. What we need is to defund and reduce the mission of the DoE until it is palpable for the public at large to accept its abolishment. When you think politics, think in decades.