Texas Senate Democrats claim to have collected enough votes to block a pilot proposal for six Texas cities. It would have given parents of children at poorly performing schools vouchers to pay private school fees.
Bush's brother Jeb, the newly-elected governor of Florida and the other half of America's hottest political dynasty since the Kennedys, seems to have had better luck. Florida may soon see the first state-wide voucher scheme.
What Jeb Bush has carefully called "opportunity scholarships" would give selected families up to $4,000 (pound;2,500) to go private. But opponents have diluted the measure to apply only to lowest-ranking pupils at the worst schools.
The Bush brothers are at the centre of new interest in vouchers, since the Supreme Court last year ruled lawful a limited voucher scheme in Milwaukee, where some 6,000 children receive them.
Voucher proposals are on the table in Pennsylvania and California. In New York and several other cities, small, privately-funded voucher schemes are sending pupils to private schools.
Vouchers would force state schools to shape up or lose out, supporters say. But there is little hard evidence on whether they improve children's education.
Isabel Sawhill of Washington's Brookings Institution think tank said polls show "a trend towards greater acceptance of the idea".
Vouchers are embraced most enthusiastically by Christian conservatives, who dream of a free-market system that would also bolster religious schools' finances.
Vouchers have also drawn support from some minority communities who want their children to escape failing inner-city schools. But they also face bitter opposition from teachers' unions and school administrators, who argue they will drain schools of money and talent.