Patients with a rare degenerative disease tried unsuccessfully to plead for special funding from the Prime Minister on Tuesday.
The patients have what is known as Pompe Disease and say the Government's drug-buying agency Pharmac has failed to help them.
There are six people in New Zealand with the disease - a genetic disorder with symptoms similar to those of muscular dystrophy.
The patients want Pharmac to fund the enzyme replacement therapy Myozyme at a cost of about $2 million per person a year.
John Forman from the Organisation for Rare Disorders says without the right treatment - which is expensive and needed for life - patients face years of increased muscle weakness followed by respiratory failure and death.
Mr Forman says four patients have had applications to Pharmac for consideration under its exceptional circumstances scheme turned down and their only hope is to appeal to Prime Minister John Key to intervene.
Mr Forman says he understands the Minister of Health is legally unable to intervene over drug funding decisions, but that Mr Key could.
Five patients, each with a wheelchair or walking stick, tried to see Mr Key in Wellington on Tuesday but were turned away by security guards on advice from the Prime Minister's staff that no one was available to meet them. Mr Key was in Tauranga.
Pharmac confirmed the applications have been declined, but says in November, its Pharmacology and Therapeutics Advisory Committee will begin considering funding the therapy.
The drug buying agency says it has boosted funding and streamlined the exceptional circumstances scheme.
The Labour Party says someone should have met the group that visited on Tuesday.