I think separating private schools from government money would be a good thing in the long run, which is why it won’t happen.
I'm not sure which private schools your are talking about or which government money. I am only familiar with the funding of the school in my parish and that my kids attend. We do have some state links for vouchers and such. But there is no money that we are dependant on from the federal government. If the Department of Education went poof! tomorrow, we wouldn't notice.
Except in the case where a private, parochial school depends on charitable donations to cover operating expenses with dwindling enrollment. To wit, the entire elementary Catholic school system. Don't underestimate the delight in the Obama White House if they managed to destroy the Catholic School system through sodomite nuptials.