The budget woes are a myth. The US spends more on education than most other countries in exchange for middle of the pack results comparable to less developed countries with far lower budgets.
The main budgetary problem is bureaucratic. The schools get more than enough money, but the teachers aren't the ones who decide how to spend it, so a teacher who wants more school supplies than are allocated has to pay out of pocket and then we get these anecdotes.
The solution is a combination of two things. First, stop trying to regulate education from the top. Let the individual teachers do it. Provide resources, don't enforce conformity. Second, let the parents choose the teachers, or more realistically, the school. Then you get competition between schools to provide the best education instead of the existing system of like it or lump it. Also, give the same money to the parents who are homeschooling. Homeschool is school and the families doing it shouldn't be financially penalized for choosing something that by most accounts gives better results.