If the health insurance mandate holds up in the courts, it might mean that Government can charge people directly for the schooling of their children and still require they be schooled or educated*.
The Government schools could start charging the rich and middle class directly to send their children to public schools? This could save a lot of money for tax payers.
One of the stronger arguments for Government schools has been that it you are to require it you will need to pay for it. People hate unfunded mandates.
A win for Obamacare would mean that Government can mandate individuals to spend on things without funding.
NOTE: Obviously Government could subsidize the poor.
*My state actually has educational requirements for home schoolers in place of school attendance. They actually requires annual evaluations of the children being home school and they must show that they have learned something.