Queenstown's Mayor says KiwiBuild is bigger than one person, following the CEO calling it quits.
But Queenstown Mayor Jim Boult is confident a new boss will be appointed soon.
"It won't happen overnight, but I'm confident the minister will find a suitably well-qualified person."
Queenstown is the site of a number of planned KiwiBuild homes, with prices in the resort town some of the highest in the country.
Mr Barclay had only been KiwiBuild CEO for six months.
National housing spokesperson Judith Collins said Mr Barclay's resignation shows what a mess the Labour flagship scheme is in.
"Answers needed. Resignation follows unexplained absence," she tweeted.
Mr Boult disagrees.
"I think KiwiBuild's bigger than one person."
Minister of Housing and Urban Development Phil Twyford has refused to speak on the matter.