The Government appears to be abandoning its promise to put 100,000 families in KiwiBuild homes in 10 years.
"We found it tougher than we expected to get the early numbers up," he told Newshub. "I don't think we can hit the 1000 target this year, and that's disappointing."
Finance Minister Grant Robertson, presently in Davos, Switzerland for the World Economic Forum, told The AM Show on Thursday said the Government was "recalibrating" the expectations for scheme, which Labour first unveiled five years before taking power.
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Asked if 100,000 was still the target, Mr Robertson said he was "not going to make that commitment today", and said it wasn't Mr Twyford that set the target.
Mr Robertson later clarified to Newshub the recalibration was to do with the workings of the 10-year KiwiBuild programme to get to the 100,000, not the final 100,000 target.
KiwiBuild was first announced in 2012 by then-leader David Shearer, with homes priced at or below $300,000. Some are now on the market for over $600,000, with the cost of land and construction rising considerably since then.
"We've managed to build some houses and get people into affordable homes," said Mr Robertson.
"Of course we want to do more and we want to do it faster, but it's a 10-year programme and it's a 10-year programme that's part of a much wider housing strategy."
Both he and Prime Minister Jacinda Ardern, also in Davos, admitted KiwiBuild's rollout hasn't been perfect. Ms Ardern told Newshub KiwiBuild was just one part of the Government's efforts to fix the housing crisis.
"For us it was about addressing housing across the board - state housing, community housing, homelessness, and of course, affordable housing. We are making progress in building housing, just not at the pace that we all want.
"But again, what I can say is while we have not been perfect, we have made considerable advancement on where we were before."
She said Mr Twyford was safe in his role as Housing Minister.
"We are building homes. We are creating emergency housing places. We are building state houses... We're not doing it at the pace we want - that won't stop us."
She declined to comment on the departure of former KiwiBuild chief executive Stephen Barclay, saying it was an employment matter.
In addition to the 33 confirmed completed KiwiBuild homes, 77 are presently under construction and another 4047 have been contracted to be built. So far 47 families have bought homes under the scheme.
Simon Bridges, whom Ms Ardern pointed out has previously admitted National's housing record wasn't perfect, on Wednesday night tweeted a single word, in all-caps: "KIWIFLOP."
Mr Robertson said that wasn't the case.
"I don't think so... There's a lot of elements to our housing policy," he said. "We're going to keep trying because we do need to build more affordable homes. No one will be more disappointed than Phil we haven't reached the first-year target, but we're going to keep trying."
Economist Shamubeel Eaqub told The AM Show KiwiBuild was "never going to fix the underlying problems of the housing market", which include "planning rules, infrastructure and funding for local government".
"The houses are so expensive that they're not affordable. The aim - that we're going to make houses affordable for the common folk - that was never going to work with this policy."
Mr Eaqub, who penned a book about the housing crisis called Generation Rent, said focusing on would-be homeowners is the wrong solution.
"The new houses are expensive. In reality, what we really want to do is increase the supply of rental stock. That's what New Zealand desperately needs - good quality rental stock that's owned by institutions and well-managed."