Around $52 million in funding for the scheme had been exhausted, and further funding was expected to be confirmed in this month's Budget.
Dr Smith also told Q+A that Auckland's Unitary Plan was "hugely important" for ramping up housing supply in the city.
"If we're going to solve the problem in Auckland, it can't be the sort of binary choice - is it up or is it out? It's actually both."
He would not say whether the Government would intervene if the council failed to approve a plan which allowed more intensified development.
The Reserve Bank said this week that Auckland needs 13,000 houses a year to keep up with demand. It is currently building 9500 houses a year.
Dr Smith said he was "always interested" in ideas for dampening housing demand.
But he ruled out toughening up the Government's "bright line test" to require capital gains to be paid if a house was re-sold within five years, rather than the existing threshold of two years.
He said a new requirement to provide tax details for every house purchase would make it "damn difficult" for investors to avoid tax on any capital gains.
"If you buy property with the intention of making a profit on its resale, you're required to pay the tax and, watch out, IRD has now got your tax number and so they're going to be very easily able to track every property that's bought and sold for investment purposes.
"And in my view, we've also invested that big lock of investment - people who are pretending they can make those investments in housing markets in Auckland without paying tax are going to get a very nasty surprise."