Within minutes, Mr Wanhill had deleted his tweets and subsequently apologised to Auckland DHB chief executive Garry Smith.
Mr Smith, who the Herald understands is leaving his job soon partly because of frustration at budget constraints, would not comment yesterday about the tweets or any other funding matters.
"Garry's view is the circumstances faced by Auckland District Health Board are the same as those faced by any other health board," spokeswoman Brooke Donovan said.
Senior doctors' union executive director Ian Powell said Mr Wanhill's tweets were likely accurate.
"I'm reasonably confident that what he was trying to say is correct."
Dr Powell said his organisation feared the funding squeeze at Auckland DHB would see cuts to frontline services.
"We would have very serious concerns because the system's been put under just too much pressure."
Labour health spokeswoman Maryan Street said Mr Wanhill's "impulsive reaction" was clearly an angry reaction.
"You don't get that agitated if there's nothing to be agitated about."
She said the funding squeeze at Auckland DHB was a common situation across all the DHBs "but we've only had one [Waikato] brave enough to come out and say it so far".
She said savings of the scale suggested by Mr Wanhill would be difficult to make "without slashing into clinical staffing".
Health Minster Tony Ryall refused to comment on Mr Wanhill's tweets but said reports of funding shortfalls and plans for clinical staffing cuts across DHBs were to be expected.
"This speculation about how much DHBs are saving or otherwise is just part of the normal process. Every year they look at how they can make savings, move their money around and improve services for patients."
Services in Auckland would not be cut, he said. "In the next year people will see more elective surgery performed, faster emergency departments, top quality cancer treatment and more help for people who smoke, and more focus on preventative measures."
DHB chief executives group chairman Kevin Snee said DHBs were clearly under some pressure "because the growth [in funding] is less than it was".
"Times are tighter but that's across the whole of the public sector. There's a lot that can be done to use the resources that we're using better."
Mr Snee, who is also chief executive of Hawkes Bay DHB, said a memo from one of his colleagues which said 35 nursing jobs there would be cut "didn't accurately reflect what was going on" and there were no plans for such cuts.
FUNDING WOES
* Auckland DHB: savings of $60 million reportedly ordered
* Waikato DHB: Savings of $30 million and likely job cuts required
* Bay of Plenty DHB: Savings of $10 million reportedly required
* Hawkes Bay DHB: Management considering cuts equivalent to 35 nursing salaries