Tax credits would provide only a temporary incentive to homeschool. Once the parent doing the homeschooling realizes the investment in time and emotional energy involved, the thrill would likely wear off.
In our opinion, vouchers would offer a more feasible alternative as it would spawn the growth and developement of new school options - still giving parents a place to SEND their kids for an education. The possibilities for education in this country are so vast and so exciting, that it's nearly unbearable to watch us limping along with the current system!
If it were up to me, I'd even take it one step further and give EVERY American citizen their public education tax money back and let the parents take responsibility for their children's education. This may sound radical, but it is currently costing (last time I saw figures) between $6,000 and $8,000 (sometimes more) per child per year to provide them with an education - and that education is often of questionable value. With a fraction of that, a parent can purchase a good private education and the rest of that money can go back into the growth of our economy.