Former prime minister Paul Keating is pushing the case for a one per cent rise in the GST so long as it's used to help fund public hospitals.
Mr Keating - who has dismissed a 15 per cent GST as "fiscal folly" - believes an increase to 11 per cent will raise the $7 billion NSW Premier Mike Baird says is needed to meet rising healthcare costs.
"If in fact it was hypothecated, as the phrase goes, so that the money can only be spent on health, well at least then members of the public would feel perhaps not so bad about it," he told Alan Jones on 2GB radio on Thursday.
States would have to ensure they wouldn't spend it on another stadium or "road to somewhere", he said.
"Premiers have got problems, I know that, but when state premiers are making the commonwealth policy for the budget you've got to start wondering where the debate is going."
Mr Keating first raised the idea of a modest increase for hospitals in an opinion piece on Wednesday, but Opposition Leader Bill Shorten rejected the proposal.
"We will not support an increase in the GST. Labor will stick to its guns," he said.
The prospect of a GST rise is spooking some federal government backbenchers.
Northern Territory MP Natasha Griggs, who has a marginal seat, admits some are daunted by community backlash on the issue.
But she says they should view this as an opportunity to talk to constituents.
"I don't think it's anything to be afraid of to talk about what's happening in your electorate and if people have got some concerns about the tax reform there's an opportunity to talk about it," she told ABC Radio.
Trade Minister Andrew Robb down played reports of dissent, saying his colleagues understood that there were several options on the table.
"I was in the party room on Tuesday and I don't think the GST was raised and I think this was because all the colleagues know that nothing has been decided," he told ABC radio.
Immigration Minister Peter Dutton said all would be revealed in good time.
"These things will be fleshed out in due course," Mr Dutton told ABC Radio.
Liberal senator Cory Bernardi, who is opposed to raising the GST, said there might be a short-term benefit, but in the long-term everyone will be paying more tax.
"I think it would be folly for the government to do it, because I think electorally it's unpopular but, two, it does increase naturally the size of government," he told ABC TV.
Senator Bernardi said he had spoken to some of his upper house colleagues about the issue. "To paraphrase Malcolm Turnbull's words, there's never been a better time to be a backbencher because we can make a contribution to the policy debate as they're shaping it going forward," he said.
