With the federal opposition and some states opposed to Labor's plans to increase Canberra's role in public health funding, the government may have to ask the Senate for permission to hold a referendum on the issue.
Asked what would happen if the upper house of parliament refused, Ms Roxon said a referendum could still be held.
"If the Senate rejects it, there are requirements to wait for a period of time and put it back to the Senate," the minister told the Nine Network on Sunday.
"But if the Senate still rejects a referendum question, the constitution allows a government to put a question even if it is rejected by the Senate.
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"Yes, there are some timing constraints about how we do that but it is possible for it to be done."
Right critical of health reforms
The coalition and Family First senator Steve Fielding have indicated they are opposed to the government's health plans.
Together, they have the numbers in the Senate to block government legislation.
Prime Minister Kevin Rudd is scheduled to put his hospitals plan before the states and territories at the next Council of Australian Governments meeting on April 11.
Mr Rudd has indicated that if they disagreed with the plan, he would seek a referendum before or at this year's federal election.
His government wants Canberra's share of public hospital funding to be increased to 60 per cent, up from 40 per cent.
No GST increase: Roxon
Ms Roxon has also ruled out increasing the goods and services tax (GST) from its present 10 per cent level to pay for the reforms.
"We have made absolutely clear the GST will not rise," she said.
"Everybody from the prime minister down is giving that guarantee."
The minister last week declined to rule out any tax rises to pay for Canberra's plans to increase its health funding responsibility.
Ms Roxon promised that smaller hospitals would be safe from closure under the government's reform plans.
"It is absolutely wrong to say anything in this plan will lead to the closure of hospitals."
Meanwhile, deputy Prime Minister Julia Gillard has vowed to cooperate with the states on hospital reform.
Prime Minister Kevin Rudd has been talking tough with state premiers over his proposed overhaul of public hospital reform, criticising those who have attacked the plan.
Ms Gillard was more conciliatory.
"We want to work cooperatively to deliver this reform plan," she told the Ten network.
She warned state governments would go broke if hospital funding was not sorted out.
Ms Gillard kept open the option of going to a referendum if agreement with the states could not be secured.
"The Australian people obviously should be the ultimate adjudicators."
