Most of the objections I heard were about putting that public money towards religious schooling (the interaction of government and religion being a fairly well-established as a partisan issue).
I'm not necessarily supporting the concept, but this seems a strained objection. It's equivocating the word "public." People who get social security (which comes from the government, and so is just as "public") can use it for religious causes and no one bats an eye.
And SCOTUS has approved vouchers funded via tax credits.
