Libertarians in general seem to forget that government is the only entity that has been specifically created to advocate for us against those who would otherwise dominate in their own interests.
Corporations certainly weren't created to advocate for us; the only reason they are beneficial at all is because the ones that aren't are killed off by market forces -- in an honest marketplace, that is, and the honesty of the marketplace depends on some form of government.
The reason government has become so abusive and negligent of late is not because government is inherently abusive and negligent, but because it has been co-opted by forces who want us to hate it so that we will dismantle it so they can do whatever they want.
That said... solving local problems by national fiat does cut both ways. When we become dependent on centralized control, we create dangerous concentrations of power. Powermongers sense these concentrations like sharks scenting blood. Any centralized control that we accept in our lives must be tempered by some kind of mechanism for overriding that control.
This is a truly difficult problem. How do we create a governance mechanism that both enforces desirable ideas such as "free and equal education regardless of fillintheblank" (which only a few people disagree with, for reasons that do not withstand scrutiny) without also enforcing really bad ideas that almost nobody likes ("No Child Left Behind" comes to mind)?
In any case, that's what we should be debating about -- how the system should work, not whether to get rid of it. If the car needs a valve job, we might talk about rebuilding the engine versus getting a new car, or possibly biking to work or taking the bus -- but we're not just going to walk away from the problem, call that a solution, and expect to still get a paycheck.
See also: government