Health Minister Peter Dutton says negotiations with crossbenchers are continuing on the GP co-payment after Labor said they would not support the measure in any shape or form.
Debate on the $7 co-payment announced in the federal budget will continue tomorrow as Parliament resumes.
People in aged care homes and a reduced payment for pensioners are also reportedly being discussed under a compromise deal.
Liberal backbencher Craig Lundy said safety nets would be in place to protect more vulnerable groups of the population from having to pay the full co-payment.
"For children under 16, the safety net kicks in at 10 visits," he told Sky News. "Concession card holders are the same."
But Labor MP Nick Champion said the exemptions would not change the proportionately greater impact on lower-income earners.
"It will hit poor people, it will hit middle-income people far harder," he said on Sky News.
"It doesn't matter what sort of exemptions they make. They can make it like Swiss cheese if they like, it will still be regressive at the end of the day."
The comments come as analysis by the Labor party found the GP co-payment and a $5 increase to prescription drugs is expected to cost individual Australians up to $300 more over the next four years.
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