Right-wing politicians have been pushing for this for decades now.
I am basically opposed, but with some caveats.
In essence, this system takes taxpayer funds and directs them toward religious education, which is illegal under the First Amendment. (The vouchers won't even cover a fraction of nonreligious private prep school, which costs a whole, whole lot more.)
All this is done on the basis of notoriously unreliable tests. These tests A) don't give an accurate measure of what kids are learning, and B) cause kids to learn less, since their whole education turns into test prep.
Finally, schools that accept vouchers can turn away kids they don't like. So, what happens to the special needs kids, the kids with serious behavioral problems, the kids whose families, for whatever reason, can't get themselves together to apply for a voucher? The public schools become a dumping ground for these "leftover" kids, but the public school now has no money left *at all* and can't meet any of their needs. So, these kids become society's problem. Think prisons, lifelong, basically, which cost a whole, whole lot more than just giving public schools the MONEY they need to begin with.
So, I'm opposed. BUT, I do think most public schools in the US are falling down on the job. I do think we need to make space for creative, innovative teaching techniques. I do think kids deserve so much better, overall, than what they're getting now. I just think vouchers will make everything worse.