Ok I was slightly wrong. The government has a right to help and supplement State education platforms but not supplant them.
"The responsibility for K-12 education rests with the states under the Constitution. There is also a compelling national interest in the quality of the nation's public schools. Therefore, the federal government, through the legislative process, provides assistance to the states and schools in an effort to supplement, not supplant, state support. The primary source of federal K-12 support began in 1965 with the enactment of the Elementary and Secondary Education Act (ESEA)."
http://www.ed.gov/about/overview/fed/10facts/index.html
So basically, the States will have to comply or not get certain funds. Which is how American government has worked for a long, long time. Little known fact: If you live in a State like Idaho you actually get more funding back to you than you are taxed for. If you live in a State like New York you get less. Simply, Idaho and other small states could not afford their infrastructure without federal funding. The same thing applies to education.