I wonder if school-choice advocates might be able to frame this argument a little better: submit legislation making it illegal for members of Congress to send their kids to private schools which are unavailable to the general public, or take a paycut so that they cannot afford private schools. When they balk, accuse them of elitism and setting themselves apart from the people they claim to serve. Then watch the schools improve, or see Congress's opinion change about school choice.
And addressing one common criticism from People for the American Way: it's not a violation of church and state to give people vouchers: not all private schools are religious, and public schools are more religious (to ABC-Anything But Christianity) than liberals like to admit. I spend my money as I see fit, and so do the parents who pay the tuition bills. No church is established by letting them do this of their own free will. If we want to make it more explicit, we could just give people tax credits instead of vouchers, it's cleaner that way anyway and we'll save money on the check printing too.
(one quick aside: I just noticed in PFAW's pdf file linked above, that they are critical of a Supreme Court decision that vouchers do not violate "church-state separation". A little inconsistent isn't it? When people criticize the Supreme Court decision concerning Roe vs. Wade, PFAW gets on their soapbox about abortion being a fundamental human right by Supreme Court decree)