But the thorny question of religion in US education has emerged as the major stumbling block. Any taxpayer subsidies to private schools will naturally end up in American religious schools, which account for about 90 per cent of private primary and secondary education.
Last month the Wisconsin Supreme Court suspended a school voucher programme in the city of Milwaukee that promised to divert up to $7m (Pounds 4.7) in funds from public schools to vouchers that could be used at the city's parochial schools, most of them Catholic and Lutheran.
Republican governor Tommy Thompson has touted the Milwaukee system as a national model. But civil liberties groups sought and won an injunction on the grounds that the scheme violated constitutional guarantees of the separation of church and state.
The Wisconsin court has yet to consider the merits of the case itself, and it could reach the Supreme Court. But last year, in another setback to reformers, the Puerto Rico courts struck down a two-year-old voucher programme on the island on the same church-state grounds.
These defeats have been serious, but have not stopped conservatives vowing change in the face of what they regard as the dismal failure of public education, particularly in inner-city areas.
Connecticut governor John Rowland this month called for a voucher system that would include religious schools.
"The poor and lower-middle class, and increasingly the middle-income earners, find themselves trapped in educational environments with which they are unsatisfied but have no alternative because of the lack of funds," he said.
In Michigan, Massachusetts and Pennsylvania, governors are also pushing voucher schemes, claiming wide public support. Ohio is the only other state, aside from Wisconsin, where local legislators have actually voted through such a programme, but it won't take effect until at least next year.
Voucher systems are bitterly opposed by the teachers' unions, the National Education Association and the American Federation of Teachers.
They say there is no hard evidence that they improve results. Public opinion, where it has been tested, seems sceptical.
In California, a vouchers proposal on a state-wide ballot was heavily defeated at the polls. Two big conservative donors, including the Wal-Mart supermarket chain, were financing an attempt to bring the issue to a second vote but have abandoned the effort for the moment.
The main beneficiaries of government funding for parochial schools would be about 8,000 Catholic schools catering for two-and-a-half million students. Catholic educators have broadly backed school-choice reforms but have avoided taking a strong position in public.
Enrolment in Catholic schools has been slowly rising in the 1990s after two decades of steep decline. Growing publicity about the poor state of public education may be part of the reason.
But the schools' constituents from a couple of decades ago - European immigrants in urban areas - have increasingly moved to the suburbs and left urban Catholic schools financially unstable and serving a clientele that is largely poor, mostly black and Hispanic and non-Catholic.