At least two crossbench senators would vote against a hike in the GST proposed by NSW Premier Mike Baird.
Family First's Bob Day and Liberal Democrat David Leyonhjelm have declared their strong opposition to increasing the GST from 10 to 15 per cent.
They believe any proposal to lift the tax should be put to a public vote.
"We know what they'll say. `We don't want to pay more tax'," the pair said in a joint statement.
"We pay enough. The states, territories and feds should stop wasting our money."
News that makes sense
Your trusted source for staying up-to-date with the world around you. Get free daily news updates and analysis, straight to your inbox.
It comes as state and territory leaders prepare to meet with Prime Minister Tony Abbott at a leaders retreat in Sydney on Wednesday, where the GST is expected to be top of the agenda.
Mr Baird wants an increase to cover a projected shortfall in future health funding.
The senators believe they have a friend on the issue in Palmer United Party senator Zhenya (Dio) Wang, who they hope will also vote against an increase.
