Terry:

I think the general threshold has been met. That is: government money = government control, or at least the ability to set significant parameters such as admissions quotas, curriculum, faculty hiring, and other significant ‘opportunity’ (including Title IX) requirements. The specific program or mechanism is less important, except to the extent that, as Daren argues, it will in practice be very difficult for non-voucher- accepting private K-12 schools to compete with those that accept vouchers. Vouchers will be voluntary in theory but mandatory in practice, due to the entirely unfair competition from other privates as well as from government schools.
Finally, I never hear pro-public-voucher, never-worry-about-the-private-schools arguments from many people who actually intend to send their kids, and do send their kids, through the public system. I would be more convinced if they were willing to argue the voucher point with their private school of choice, where I think it properly belongs, or if they simply let their kids tough it out through the public school system, pre- or post-secondary, that they defend. I’m not sure either is the case. Therefore I remain a sceptic and a critic on the public money/public control issue, whatever the analogy one chooses to apply.