Keytruda was registered in New Zealand last September but Pharmac's clinical professionals have classed it a "low priority" until it gets better data on survivability.
Leisa Renwick is now well enough to have organised the petition, which will be received by her local MP, Simon Bridges.
"He is sympathetic but he emphasises that he is receiving the petition as a Member of Parliament, not as a minister, that Health is not his portfolio and he can't intrude on the Minister of Health's portfolio."
She said she was not happy that Health Minister Jonathan Coleman did not have the time to meet the petitioners "yet when you look at his Twitter feed, he seems to be taking his responsibilities as Minister of Sport very seriously".
Her message to Dr Coleman was one of responsibility: "The fact is he has people who are dying and will die if they are not treated ... the medicine won't work for everyone but, at the moment, they don't even have the chance to fight."