The government had hoped to get rid of the Schoolkids Bonus – worth $820 a year for a high school student and $410 a year for a primary school student – as part of its repeal of the mining tax, but had been blocked by the Senate.

Key Senate crossbenchers said they wanted the bonus to remain but were willing to consider amendments including restricting it to low-income families and targeting it at spending on education.

The bonus had been controversial since its introduction. Liberal frontbencher Christopher Pyne warned the payments could be spent on "plasma televisions, booze or be run through poker machines and into the pockets of poker machine barons" rather than on education.

Smith Family chief executive Lisa O'Brien said: "Helping families with a child's education long term takes more than just a one-off payment twice a year. You need to have a framework behind it to deliver long-term results.

"There is no framework around the Schoolkids Bonus to make sure parents are supported on how they might best contribute to a child's education and development. There is also no ongoing evaluation of its success."

A revamped Schoolkids Bonus could be spent on uniforms, books, school excursions, computers and extracurricular classes, Dr O'Brien said. Parents should also be able to have access to mentoring and support programs.

The Smith Family's sponsorship program for disadvantaged students, Learning for Life, tracked educational and employment outcomes for students receiving financial assistance.

Abolishing the bonus would save the budget $5.2 billion over four years, based on figures from the Parliamentary Library.

Independent South Australian senator Nick Xenophon said he was open to making the scheme more tightly focussed on educational spending.

"I have been critical of the Schoolkids Bonus," he said. "I thought it should have been a voucher system for books or uniforms though apparently there are concerns about the costs of implementing it."

Mr Xenophon said amending the scheme, rather than ditching it all together, would be welcomed as a "pragmatic" move by the government.

Family First senator Bob Day said: "I'm up for discussion on varying the Schoolkids Bonus, including means testing and other restraints. It's not a die-in-the-ditch policy for me."

He said he would use support for a new scheme as a "bargaining chip" for his own policy demands, including workplace deregulation and ditching the government's proposed paid parental leave scheme.

Palmer United Party senator Jacqui Lambie had said too many wealthy families were eligible for the scheme and money went to parents who received Family Tax Benefit Part A, the Disability Support Pension, carer and other government payments.

It replaced the Education Tax Refund, which required parents to keep receipts and claim them through their tax returns.