PHOENIX — State lawmakers are making a new attempt to provide taxpayer-provided dollars to all 1.1 million students in Arizona schools to help their parents pay to instead send them to private and parochial schools.

The proposal by Sen. Debbie Lesko, R-Peoria, would dramatically expand what has been a small program now reserved for students with special needs and those in failing schools. It would create what amounts to a universal “voucher” of state funds that could be used to pay tuition and fees at other schools.

Lesko said this would not lead to a mass exodus of children from public schools.

Sydney Hay, lobbyist for the American Federation for Children, which pushes such programs nationwide, said it’s not really a voucher, as parents are free to instead use the dollars to purchase services for their children, including specific classes and tutors. But these essentially have to be parents who home-school their children, as the funding is not available to anyone who attends a traditional public or charter school.

And the system would be set up so that if parents have state money left over they can bank that, even setting it aside for a child’s college education.

Lesko pointed out existing law caps these vouchers at 0.5 percent of all students, a figure that comes out to about 5,500 students. But that cap self-destructs in 2020 — about the same time as Lesko’s four-year phase-in of vouchers for all would take effect. Lesko was noncommittal about supporting a new cap at that time.

Her legislation is the latest effort to expand what started out as a small program in 2011 to help parents of children with disabilities. It provides the equivalent of 90 percent of what would be state aid to send a similar child to a public school. Since that time, lawmakers have extended the program to any child in a public school rated “D” or “F” by the state Board of Education.

A similar measure faltered last year.

This year could be different. Gov. Doug Ducey has pronounced himself a strong supporter of “school choice,” and is scheduled to appear Thursday at a School Choice Week celebration at the Capitol.

Also, Lesko has added a sweetener of sorts to this year’s version: Schools would be required to test students who are attending with vouchers and report the results to the parents. But Lesko said she does not believe it is necessary for private and parochial schools to report the test results to the public, even though taxpayers are funding the education.

Chris Kotterman, lobbyist for the Arizona School Boards Association, said none of that makes the idea more acceptable.

“The private schools are a parent’s choice and they’re a legitimate choice,” he said. “But the state has an obligation to fully and adequately fund its primary mission, which is the free public schooling of all the students. And we’re not doing that right now,” he said, with teachers “leaving in droves” and buildings and buses in disrepair.

Kotterman said the state should not be diverting dollars away from public schools.

Lesko pegged the average voucher at $5,200 for students without special needs. Using that figure, Lesko said that’s still cheaper than the more than $9,529 it costs to educate the average public-school student.

But Kotterman said that figure is misleading because it also includes local and federal funds as well as bonds and overrides.

He said all schools depend to some degree on locally raised revenues. And that means many schools get less than that full state-aid formula.

Put in its most extreme example, he said, the state provides no student aid for Cave Creek schools, since that district raises more than enough from local revenues. But if a student moves from a Cave Creek school to a private or parochial school, the state is now on the hook for voucher money it never was obligated to pay before.

There is the parallel question of whether there would be any long-term savings to the state.

Lesko said her legislation qualifies only those who are “switchers,” meaning they came from a public school. But she acknowledged a family that already intended to send a child to a private school could qualify for a voucher simply by sending the child to a public-school kindergarten for one year.

The bottom line, said Lesko, is choice. “This is another option for students and parents,” she said. It’s an increasing national trend, she said, noting the nomination of Betsy DeVos, a long-time proponent of vouchers, to President Donald Trump’s Cabinet.