Another of its policies, a promise to pay schools which do not ask parents for donations, gained support in the poll.
National has pledged $359 million for a scheme that would pay the best teachers and principals more.
Labour countered by promising to use that money to instead hire 2000 more teachers and reduce class sizes.
Asked about those policies, 61 per cent of those polled said the money was better spent on trying to improve teaching standards.
Thirty-five per cent thought it should be used to cut class sizes.
Yesterday, Labour education spokesman Chris Hipkins said he rejected the premise of the question.
It did not convey that Labour's plan to hire more teachers would also allow for teacher training, and that its education policy was strongly focused on teacher quality.
That included establishing an advisory service to provide mentors and share best practices, and pre-screening entry into teacher training programmes. "Smaller class sizes do lead to better teaching. The teacher gets more time with each student, student behaviour is improved, and studies clearly show that students in smaller classes spend more time focused on the task at hand.
"Smaller class sizes also allow the teacher more time to reflect on and improve their own practice."
Labour's class size policy followed other announcements, including paying schools which did not ask parents for donations and subsidised netbooks or laptops for students.
Education Minister Hekia Parata said the survey showed parents recognised the worth in the initiative.
"Parents have great knowledge about what makes a difference for their kids' learning, and it is about the quality of learning that happens in their child's classroom."
This month the Post Primary Teachers' Association conducted its own survey which showed that more than eight in 10 New Zealanders wanted secondary school classes at 25 or lower.
The union also supports National's Investing in Educational Success plan, in contrast to the strong opposition from the NZEI primary teachers' union.
The Herald-DigiPoll survey of 750 voters was taken between July 10-17.