Mahboobeh Mirshahi, an organiser of the Melbourne sit-in, said there were between 10 and 12,000 asylum seekers in legal limbo with no clear pathway to Australian residency.
The former coalition government established an assessment scheme to resolve the visa applications of more than 30,000 asylum seekers who arrived by boat between 2012 and 2014.
The fast-track system restricted the types of visas people could access and limited their avenues of appeal.
The policy has been widely criticised for failing to live up to its name. On average, it takes up to six years for people to receive their first temporary visa.
"We've been here for more than a decade and all our cases are stuck between the immigration assessment authority and the Federal Court," Ms Mirshahi, who came by boat in 2013, told AAP.
The 42-year-old nurse left Iran with her family to escape religious discrimination and they were later detained on Christmas Island before being released into the community on bridging visas.
"The waiting is killing us. We urgently need action from the government," she said.
Ms Mirshahi welcomed the government's decision earlier this year to grant permanent residency visas to 19,000 asylum seekers on temporary protection visas and asked for the minister to take similar action for others on bridging visas.
Her daughter Tanya said feeling different from her peers because of visa insecurity had taken a toll on her mental health.
"Being a teenager is already hard enough but advocating for our rights constantly has added a whole bunch of stress onto my life," the 16-year-old high school student said.
"I've been here since I was six years old so I consider myself fully Australian.
"I grew up with everything my peers grew up with like ABC Kids ... but I just feel kind of alienated from my friends because they have some of the rights I don't have."
Her mother, who works in a pathology lab, said she hoped the government would capitalise on the skills of refugees by granting them permanent visas.
She worked as a frontline worker at the height of the pandemic during lockdowns in Victoria.
"I stood up with Australia at a time of great risk and hardship and I expect the Australian government to stand with me."
AAP contacted Ms O'Neil for comment but did not receive a response.
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