Motoring Enthusiast Party senator Ricky Muir says his "ears are open" to negotiations on the $7 GP co-payment, a day after his political partner Clive Palmer claimed to have killed off the charge.
Senator Muir, who has formed a loose alliance with the Palmer United Party, says under its current form the Medicare co-payment is "very hard to support".
But he is willing to consider an alternative model for the payment.
"My ears are open," he told reporters after a meeting with his PUP allies in Canberra.
"I'm happy to listen to what people have got to suggest."
Mr Palmer has declared the co-payment dead, saying his party had unanimously decided not to support a co-payment "of even one cent".
Labor and the Greens are also opposed to the unpopular payment, and without PUP support it will be blocked in the Senate.
The PUP leader insists his party won't be changing his mind on the co-payment.
"As far as we're concerned it's dead," he told reporters.
"We've got to do what is best for people that live in this country."
However, the government won't concede the budget measure is a no-goer, with Health Minister Peter Dutton saying the public positioning of crossbenchers differed from what they were saying in negotiations.
Labor leader Bill Shorten is not claiming victory on what the opposition has dubbed the "GP tax".
"What I know is this government will do anything to get its way," he told reporters in Queanbeyan.
"This is a government who never give up ... trying to be unfair."
Mr Dutton refused to comment on private discussions with the crossbench but said Senator Muir was "very reasonable" and "very keen to talk about health issues".
Negotiations would continue in good faith, he told reporters in Canberra.
"I really do believe that people understand that Medicare is going to collapse under its own weight if we don't have the sorts of changes that are needed," he said.
Mr Dutton said he believed the government could reverse public opinion on the deeply unpopular co-payment.
"I think we can win this argument, because in the end people do want a strong Medicare," he said.
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