The Grounded Kiwis group is hoping its calls for changes to managed isolation are heard and that the threat of Omicron does not cause delays.
A petition with 22,888 signatures was delivered to Parliament today, calling for MIQ to better align with the Bill of Rights.
National Party Covid-19 spokesman Chris Bishop called MIQ a "lottery of human misery" that had gone on "far too long" when he was handed the petition on Parliament's forecourt.
"It is legally dubious, it is morally wrong, and the sooner we can end MIQ the better."
Border changes are set to start on January 16, 2022, when fully vaccinated New Zealand citizens and residents travelling from Australia are allowed to isolate at home for seven days instead of at an MIQ facility.
Bishop was aware of the threat of the Omicron variant but hoped the Government would not backtrack on the reopening dates.
"We can't remain the hermit kingdom forever. We have to start reconnecting to the world."
National Party immigration spokeswoman Erica Stanford said people overseas recognised a risk-based approach was still needed.
"I guess they're sitting overseas and looking at Aucklanders, who can travel the country [from December 15], where they can't get home," she said.
"And I think that's where they're really aggrieved, and upset, and anxious, and depressed."
The petition also had the support of Act and the Greens, with David Seymour and Elizabeth Kerekere standing alongside National this morning.
Seymour said New Zealand had had "an abundance of caution in our Covid response".
"Where is the abundance of kindness for these people and where is the balance between Covid-19 and every other risk that New Zealanders face to their welfare?"
Later in the day, Seymour said the current MIQ situation "verges on a form of torture" - a comment he did not think went too far.
Kerekere said issues related to MIQ "must stop" and that she, Bishop, Stanford, and Seymour were "committed to keeping on representing this in the House and every time we get the opportunity".
She said it was not just a Bill of Rights issue, but also of the Treaty of Waitangi.
Sarah Romans, who recently arrived back in New Zealand, was among the small crowd at Parliament for the handing over of the petition.
She thought there should be home isolation for overseas arrivals.
"I was double vaccinated before I left in July, so I was the ideal candidate to come home. I live alone and isolate in my home."
Alexandra Birt, one of the Grounded Kiwis petition organisers, made a virtual appearance from MIQ, where she arrived on Monday.
Speaking to RNZ, she said she thought some people framed Covid-19 at the border as an "us" and "them" issue: those overseas seen as the infectors, those in New Zealand as the protectors.
"We are 100 per cent against that approach," she said.
"We say we're all part of the 'team of 6 million' - it's not a team of 5 million - and we're all working together to achieve the same aim; it's about getting people home in a safe way."
Covid-19 Response Minister Chris Hipkins said the Government heard peoples' concerns about the effect of border restrictions, but the restrictions had also been key to the outcomes of New Zealand's pandemic response.
"We're trying to provide as much certainty as we can in a very uncertain environment ... the global pandemic hasn't finished and there are still a few twists in the road ahead."
He said the Government would work "as hard as we can to provide certainty to those families who have been separated by the border restrictions".