Katie Newmark brings us up to date. Some folks would apparently prefer direct aid to vouchers. This isn’t as paradoxical as it sounds, since the aid would follow students in a manner analogous to vouchers, thereby also avoiding the ostensible First Amendment problems with direct aid. The reasoning supporting this program can be found in Mitchell v. Helms, which upheld limited per capita aid to parochial schools in--guess where?--Louisiana. The limits, predictably, came from Sandra Day O’Connor helped by Breyer), while Thomas, Scalia, Rehnquist, and Kennedy would have supported a much further-ranging program of non-discriminatory aid.
For the record, I think Katie is right about the politics of this proposal. It is a risk, but because it’s less likely to empower parents in an "addictive" way, it may have less long-term influence than a straight voucher program.