The government is expected to put Medibank, Australia's largest health fund, on the market next year.
But Labor's health spokeswoman, Julia Gillard says the government might postpone the sale until after the next federal election, after a recent poll found nearly two-thirds of Australians oppose the move.
Ms Gillard warns that privatising Medibank could lead to an increase in premiums for its customers.
"Sixty three percent of Australians are opposed to the sale of Medibank Private and almost half of Coalition voters are opposed to the sale of Medibank Private," Ms Gillard said.
"The government's advocacy of this sale is so pathetic, it hasn't even convinced its own voters that the sale should go ahead."