Between October 2021 and April this year, workers and patrons were required to show proof of double vaccination against COVID-19 to continue to participate in the Victorian economy.
Eric and Tracey Wilson, who are self-representing, want the Federal Court to decide whether their rights were violated by the mandate.
They claim the vaccinated economy was "aided by coercion", and labelled government statements that double vaccination would lead to zero or lower hospital admissions as "pure fiction".
"The whole basis of the vaccinated economy was fanciful," Mr Wilson told the court during a hearing on Friday.
"It is more about the economy than the wellbeing of Victorians."
The Wilsons argued the mandate had violated their freedom under the Australian Constitution, the Magna Carta and the Charter of Human Rights and Responsibilities.
"The whole scheme is unconstitutional," Mr Wilson said.
Lawyers for both levels of government rejected all of the Wilsons' claims and argued the case should not be heard by the court.
Christopher Tran, for the State of Victoria, said the mandate was proportionate to the response needed to the COVID-19 pandemic.
The couple have been trying to raise money for their legal action online, but only $400 has been donated of the $120,000 they claim is needed.
Commonwealth and state government lawyers pointed out that the laws have changed since April 2022, allowing workers to be unvaccinated.
But Ms Wilson, who lost her job in regional Victoria because she refused to be vaccinated, said she continued to suffer hardship from the mandate.
"What we have been through and the hardship we're still facing because of that hasn't finished," she said.
"My job has been replaced because I wasn't there. They did a shuffle of their system, which meant that I became redundant."
Justice Lisa Hespe reserved her decision.
