As a father of five children aged 8 to 16 – Max, Henry, Eve, Leo and Archie – he saves thousands of dollars a year through the federal government voucher scheme that focuses on prevention and early intervention.

But his family is in the minority: only a third of eligible children have accessed the scheme since it started in early 2014.

That's part of the reason the Turnbull government wants to scrap it: Health Minister Sussan Ley calls it "under-utilised".

But Grenville reckons it is under-utilised because it is under-promoted.

"It isn't pushed at all, there's nothing at schools," he says. "Other parents are bewildered when I tell them about it. They just didn't know it existed."

The Grenville family dentist, Victorian President of the Australian Dental Association Andrew Gikas, agrees. And for those who do know about and use the scheme, many may not realise the government is trying axe it.

The ADA is lobbying Labor and the crossbench to stand up for the means-tested CDBS, which is facing the axe as part of the government's omnibus savings bill – due for debate in Parliament this week.

The association believes the government's proposed replacement – the Child and Adult Public Dental Scheme – will strip millions a year from the system and leave rural and remote communities in the lurch. It will be delivered by the states through the already-stretched public system.

"The CDBS is an invaluable and unique scheme with a strong focus on early prevention," says Dr Gikas. "If the government pushes on with this change we'll see larger waiting lists, increasingly expensive emergency treatments and a general decrease in our ability to focus on prevention."

Greens Leader Richard Di Natale says cutting the CDBS will rip $1 billion of dental care away from kids who need it most. And Opposition leader Bill Shorten appears to be prepared to wave it through, he said.

"Labor needs to choose – stand with the Greens on this issue or cave to the government's unfair cuts to kids' health," Senator Di Natale said.

Labor is refusing to commit either way but says it is "scrutinising all measures" in the government's omnibus bill.

"Labor established the CDBS in response to alarming evidence about the oral health of Australian children," health spokeswoman Catherine King said. "The government's own health department says the scheme has been a success, with the only failure being the government's refusal to promote it."

For the Grenvilles, there's no doubt what it will mean if the cut goes ahead.

"We just won't be able to go to the dentist as much," Mr Grenville says. "That means poor dental health, which will probably cause us more financial woes down the track."