On Tuesday, after a legal fight, the Indiana Supreme Court upheld the state’s voucher program as constitutional. This month, Gov. Robert Bentley of Alabama signed tax-credit legislation so that families can take their children out of failing public schools and enroll them in private schools, or at least in better-performing public schools.

In Arizona, which already has a tax-credit scholarship program, the Legislature has broadened eligibility for education savings accounts. And in New Jersey, Gov. Chris Christie, in an effort to circumvent a Legislature that has repeatedly defeated voucher bills, has inserted $2 million into his budget so low-income children can obtain private school vouchers.

Proponents say tax-credit and voucher programs offer families a way to escape failing public schools. But critics warn that by drawing money away from public schools, such programs weaken a system left vulnerable after years of crippling state budget cuts — while showing little evidence that students actually benefit.

“This movement is doing more than threaten the core of our traditional public school system,” said Timothy Ogle, executive director of the Arizona School Boards Association. “It’s pushing a national policy agenda embraced by conservatives across states that are receptive to conservative ideas.”

Currently, 17 states offer 33 programs that allow parents to use taxpayer money to send their children to private schools, according to the American Federation for Children, a nonprofit advocate for school vouchers and tax-credit scholarship programs that give individuals or corporations tax reductions if they donate to state-run scholarship funds.

To qualify, students generally must fit into certain categories, based on factors that include income and disability status. Georgia students do not need to meet any specific criteria to receive tax-credit scholarships. And under the income criteria set for Indiana’s voucher program, nearly two-thirds of the state’s families qualify.

The Arizona Legislature last May expanded the eligibility criteria for education savings accounts, which are private bank accounts into which the state deposits public money for certain students to use for private school tuition, books, tutoring and other educational services.

Open only to special-needs students at first, the program has been expanded to include children in failing schools, those whose parents are in active military duty and those who are being adopted. One in five public school students — roughly 220,000 children — will be eligible in the coming school year.

Some parents of modest means are surprised to discover that the education savings accounts put private school within reach. When Nydia Salazar first dreamed of attending St. Mary’s Catholic High School in Phoenix, for example, her mother, Maria Salazar, a medical receptionist, figured there was no way she could afford it. The family had always struggled financially, and Nydia, 14, had always attended public school.

But then Ms. Salazar, 37, a single mother who holds two side jobs to make ends meet, heard of a scholarship fund that would allow her to use public dollars to pay the tuition.

She is now trying to coax other parents into signing up for similar scholarships. “When I tell them about private school, they say I’m crazy,” she said. “They think that’s only for rich people.”

These state efforts come at a particularly challenging time for public schools. Their budgets suffered severely during the recession, and they are now facing pressure to conform to new curriculum standards and to evaluate teacher performance.

“We’re not providing adequately now,” said Dennis Van Roekel, president of the National Education Association. “Why would you take away” financing from public schools?

In 2002, the Supreme Court ruled that school vouchers did not violate the Constitution’s separation of church and state, even though many families use the public money to send their children to religious schools. Many states, however, still have constitutional clauses prohibiting the financing of religious institutions with public money, which is why some of the programs face legal challenges. Voucher opponents also have filed suits based on state constitutional guarantees of public education.

Beyond Indiana, the Supreme Court in Louisiana heard an appeal this month by a group of parents who are currently using vouchers and the Black Alliance for Educational Options, an advocacy group, after a lower court upheld a challenge to the state’s voucher program. They argued that children enrolled in failing public schools had the right to a high-quality education.

“What we’re dealing with is what public monopolies always give us, which is low quality at a very high price,” said Richard Komer, a lawyer with the Institute for Justice, a libertarian public-interest law firm that represents the pro-voucher groups in Indiana and Louisiana. “The idea is to try and break that cycle, because what we’ve been doing in public education since the beginning of time is rewarding failure.”

Critics say schools that accept vouchers or tax credit scholarships often filter out students with special needs, and that families already sending their children to private school use the public programs to subsidize their tuition. It is also not clear that students who attend private schools using vouchers get better educations, as many do not have to take the annual standardized tests that public school students do. Research tracking students in voucher programs has also not shown clear improvements in performance.

“At the same exact time as accountability and transparency seem to be the total watchword for how are we spending these dollars in an austerity-ridden environment,” said Randi Weingarten, president of the American Federation of Teachers, “there’s absolutely no accountability with vouchers.”

Mr. Komer at the Institute for Justice called for a shift of focus. “We happen to take the view that parents know best,” he said, “and are the best accountability measure to make sure that things are done properly for their kids.”

In Arizona — which, over the past five years, cut more of its K-12 budget than any other state, according to the Center on Budget and Policy Priorities, a policy research group based in Washington — charter schools are ubiquitous and school districts have open borders, so children are free to go to school wherever they want.

Dr. Ogle, of the Arizona School Boards Association, said, “The arguments that you need to have more options is superfluous.”

But the savings accounts have many powerful supporters, including Arizona’s governor, Jan Brewer. Unlike vouchers, these accounts allow the money to follow the child from one school year to the next. (Scholarships total roughly $3,500 a year, or the state’s portion of school per-pupil funding.)

“It will be the end of schools that don’t perform, and that’s a blessing,” said Darcy A. Olsen, president of the Goldwater Institute, which designed the program and led a robust lobbying campaign to pass it in the Legislature. “We’re not doing anyone any favors by keeping schools afloat that don’t teach children how to read.”

The school boards association and the state’s teachers union, among others, have challenged the savings accounts in court on the grounds that they violate a constitutional amendment banning spending public money on private schools. (Direct vouchers, begun in 2006, were deemed unconstitutional in 2009 for that reason.)

In January 2012, a Superior Court judge in Maricopa County, which includes Phoenix, upheld the savings accounts, though the plaintiffs appealed the ruling. Oral arguments were heard last month. A decision is pending.