"Analysis from the Council of Trade Unions has revealed a $1.7 billion funding gap in health. Now we hear DHBs don't have enough money to pay staff their promised salary increase."
She said Minister of Health Jonathan Coleman had a "crisis in his portfolio".
The statement quoted PSA board member and mental health worker Andy Colwell as saying members were "reluctant to take action".
"We want to deliver quality care every day - but the DHBs' proposals to cut our pay and conditions while not addressing our concerns about workloads and resourcing leave us no choice".
A spokesman for the three health boards said they were confident the issues would be resolved before the strike took place.
He said the health boards believed they had put forward a fair offer.
A spokesman for Mr Coleman said: "It's totally incorrect for the PSA to claim there's a $1.7 billion funding gap in health as funding has increased by $4 billion under this Government to a record $15.9 billion."