Mr Joyce, however, doubted whether the money would stretch that far.
If the houses were built for $500,000, the capital would have to be recycled 25 times, he said.
"That is simply fanciful. They would have to buy the land, get the consents, build the infrastructure, design 4,000 houses, build 4,000 houses, and sell 4,000 houses all in five months. Not just once but 25 times."
Mr Joyce said Labour could also get tripped up by planning and infrastructure delays which were affecting all developers.
The Government says councils' planning and consenting rules are a key factor in slowing housing supply.
Labour's finance spokesman Grant Robertson said National ministers were now "flailing about" and contradicting themselves.
Yesterday, Mr Joyce had originally described Labour's new housing policies as "an endorsement of the Government's approach with a few tweaks to it".
Mr Robertson said that in the same breath he had said it could not be done.
"Steven Joyce knows full well that KiwiBuild works by the Government fronting up to build affordable homes, and using the profits from their sales to re-invest in building more affordable homes."
United Future leader Peter Dunne said both major parties' housing policies were "scattergun" and "piecemeal".
"National says Labour is just copying its policies and then, curiously, that it will not work - and Labour announces a so-called affordable housing package, without any indication of how young families will be financed into these homes.
"It all sounds like the Mad Hatters Tea Party, if it were not so serious."
Mr Dunne reiterated his call for a cross-party housing summit - a proposal which has previously been rejected by the Government.
