Thousands of public school students in Virginia could have the option of taking all of their classes on a home computer in what is known as a “virtual school” — instead of making the daily trek to a building with bells and defined class times.

Gov. Terry McAuliffe is mulling whether to sign House Bill 8, a largely Republican-backed piece of legislation that would allow Virginia to join Florida, Ohio and 28 other states in providing 12 years of public education in what enthusiasts describe as a “classroom without walls.”

In the face of cautionary research suggesting students in virtual schools fall behind their peers in traditional schools, the General Assembly is pushing to make a statewide virtual K-12 school a reality. The House of Delegates approved the bill on a 58-40 vote and the Senate passed it 23-17 before sending it to the governor.

If the governor signs it, the legislation would create a separate state board that would be required to open a separate, tuition-free, K-12 virtual public school beginning in the 2018-19 school year.

While advocates see it as a move boosting educational choices for parents and their children, critics view the measure as possibly stripping state support and students from traditional public education.

Of the 1.2 million students who attend public schools across Virginia, only a small fraction could participate. The legislation essentially sets up a pilot project that would limit enrollment to 5,000 students at a total cost of around $25 million a year. All the virtual classes would have to meet Standards of Quality and Standards of Learning requirements.

To fund the virtual school, the legislation would shift state money that typically would go to the students’ local school districts to private vendors the board would hire and pay to provide online classes.

Shifting state funds now going to public school to pay private vendors for a virtual school is a sore point for critics who fear such operators would put profits ahead of the welfare of students.

So far, Gov. McAuliffe, an advocate of school reform, has been mum about his intentions ahead of the April 10 deadline to sign or veto the bill. Based on the relatively close majorities by which the bill was approved by the General Assembly, the legislature unlikely will have the votes needed to override the governor’s veto should he decided to kill the legislation.

Delegate Richard P. “Dickie” Bell, R-Staunton, the bill’s author and the leading proponent, is optimistic. He told reporters following a March10 meeting with the governor that Gov. McAuliffe “supports virtual education.”

However, the governor is facing calls for a veto from many of his Democratic allies at the State Capitol, including the 18-member Legislative Black Caucus, and from associations representing public school boards, superintendents and teachers.

Robley Jones, director of governmental relations for the Virginia Education Association, is among those urging the governor to kill the bill.

Along with siphoning off needed public school funds, Mr. Jones notes that the students who enroll could suffer. He points to the problems that have plagued virtual schools in other states, including “low graduation rates, poor academic performance and high dropout rates.”

“Most students do not have the time management skills and discipline” needed to be successful in a virtual school, he said. He also is concerned virtual school could limit development of social skills, including learning to work with others.

Mr. Jones noted that a September 2015 report by the Joint Legislative Audit and Review Commission, a state government watchdog agency, urged caution about a quick expansion of virtual education, calling instead for the state to continue its go-slow approach.

“Because there is limited research on the effectiveness and cost of online learning programs in Virginia,” JLARC concluded in the 74-page report, “the state should use a data-driven, incremental approach to expanding access to fully online programs,” a recommendation Delegate Bell and other legislators largely ignored.

The bill also ignored another JLARC concern about the lack of any “accurate statewide method to estimate how much funding the state should provide for virtual learning.”

Somewhat surprisingly, advocates for home schooling — the practice of parents taking their kids out of public schools and doing the teaching themselves — are unimpressed with the virtual school concept and see little benefit for their approach.

Yvonne Bunn, executive director of the 33-year-old Home Education Association of Virginia, said the data she has reviewed indicates a virtual public school would not be a good approach for the organization’s members.

She said parents who home school — nearly 39,000 Virginia children currently are home schooled — are heavily involved and use a host of tools, from computers to textbooks. She said the most important element is the “one-on-one interaction” between the parent and the student, enabling quick assessments and corrections and avoiding the restrictions the public schools —including a virtual school — would impose.

While Virginia has offered virtual classes since 2002, most are provided in traditional schools. Beginning with ninth-graders in 2013, every high school student must take at least one online course to graduate, though it can be a non-credit course.

This year, the Virginia Department of Education piloted the first virtual high school, but limited enrollment to 100 students statewide. Students were required to apply through a guidance counselor at their high school.

Delegate Bell, a retired special education teacher for Augusta County Schools, found that too limited. Having advocated for virtual K-12 education since 2010 when he became a legislator, he found VDOE’s effort too limited, a main reason he pushed the current bill.

In Delegate Bell’s view, computer-based education is ideal for young people who don’t perform well in a traditional school. He has argued that some students do better work on a computer, and that virtual school is an alternative for students who are bullied at the traditional campus.

Convinced of his position, he generally has ignored the limited findings urging caution, including the yearly reports on virtual education the National Education Policy Center (NEPC) in Boulder, Colo., has produced since 2013. Those reports provide the only limited data available on a national basis.

According to the center, public school virtual education has been growing. Currently, about 245,000 students are enrolled in 338 virtual schools operating in 30 states, up 22 percent from the previous year, but still a tiny number compared with the 50 million students enrolled in traditional schools, the center found.

Despite legislative enthusiasm, NEPC has found reason for caution, finding that only 36 percent of virtual public schools achieved “academically acceptable ratings

and that only about 44 percent of students at full-time virtual high schools graduated in four years, compared with the national average of 77 percent.

More attention likely is to be paid to such concerns if Gov. McAuliffe allows the virtual school to move beyond the talk stage.