The laws about homeschooling in Ohio won't be changing. What will change if Gov. Strickland's budget cuts hold is that virtual schooling will adjust/change/decrease.
Strickland plan would slash online-school funding
Under the governor's two-year budget proposal, the state would provide about $1,500 in per-pupil aid to online charter schools, down from the roughly $5,700 they now receive, according to charter-school supporters.
Since the law governing homeschooling (not just unschooling) isn't in question, the budget cut has nothing to do with homeschooling.
Also, concerning "school choice" (how kids are educated), the NCLB emphasis on "school choice" is probably the culprit in making people think that any kind of schooling ought to be paid for by taxpayers, although that doesn't seem to be the intent.
U.S. Department of Education
School Choices for Parents
If a child attends a Title I school that has been identified by the state for school improvement, corrective action, or restructuring, parents can choose to send the child to another public school that is not so identified.
From this reading, NCLB school-choice is choosing from among public schools, not to provide every child with a smorgasbord of 'menu items' to choose from.