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On Saturday, Twyford and Prime Minister Jacinda Ardern welcomed 18 families to their KiwiBuild homes in Papakura. Among them were Fletcher Ross and Derryn Jayne, who took ownership of a four-bedroom home on Regiment Way costing $649,000.
The development is the first to be completed in the Government's plan to build 100,000 homes in the next decade, but it has lead to questions about whether a graduate doctor or a marketing manager should be eligible for KiwiBuild.
A comment on Twitter last night by National's housing spokesperson Judith Collins has now sparked a war of words between her and Twyford, while the couple have taken their social media profiles offline.
Commenting on an Instagram shot of Ross and Jayne where he tells her "204 countries + 7 seas and I had the privilege of meeting you", Collins said: "204 countries - maybe doesn't need taxpayer support."
Twyford said this morning that Collins' post was "essentially inciting victimisation of a young couple who have just bought their first home".
"They didn't sign up for that. They feel bullied because of Judith Collins' actions. And I think her actions show the toxic culture in the National Party that Simon Bridges has failed to do anything about."
He said the couple had felt so bullied that they had taken their social media profiles offline.
But Collins hit back on Twitter, saying she had not trolled anyone's online personal pages, and even applauded the young couple for buying a new home.
She said she had also asked Radio NZ to remove "this false & defamatory statement" from Twyford.
National leader Bridges denied that his MP had trolled or cyber-bullied the couple, saying the situation was merely a reflection of the pressure Twyford was under.
"She's pointing out really poor eligibility criteria," he said.
Collins had also pushed back against the notion she had misconstrued a romantic message between the couple, Bridges added.
Last night Collins said that KiwiBuild should be targeted at those who need it most, and it should come with an obligation on people to help themselves.
"KiwiBuild does neither. With billions of taxpayer dollars involved and significant personal benefit to lottery winners at the expense of taxpayers, there should be stringent eligibility criteria."
Twyford said KiwiBuild wasn't just for the poor, but about building affordable homes.
"Two teachers in Auckland who could take home $160,000 a year before tax, they are effectively locked out of the market because the gap between house prices and incomes was allowed to get so out of control.
"That's why we've set the income threshold at $180,000 [a year] for a couple in Auckland and Queenstown ... There's a whole generation of young New Zealanders out there, many of whom are in good jobs, earning good money, and they cannot buy their own home in places like Auckland."
He said the recipients of KiwiBuild homes in Papakura were a "slice of middle New Zealand".
"There's a concrete worker, a student, a stay-at-home mom, a designer, someone who works in marketing."
Ardern said middle-income New Zealanders who were not eligible for Government support were also locked out of the property market.
"From the families that I canvassed [in Papakura], there was a range of different careers in the mix there.
"Many of them commented that they had not been eligible for any other form of support, that they also hadn't been able to get on the property ladder.
"And that is what KiwiBuild is about ... This in and of itself isn't going to be the thing that helps those who are on our lower incomes from getting into the housing market.
"For that we're looking at the possibility of shared equity schemes and we also have a programme around public and state housing."