All tertiary students are ineligible for student loans after seven years of full-time-equivalent study.
A medical degree takes six years to complete. But medical schools select more than 30 per cent of students from applicants who have previously completed a degree, meaning those students cannot access a student loan in their final years of study.
The capped policy was introduced in 2011 and the NZMSA says it will affect students from late this year.
Mr Joyce said, overall, the capped policy worked well and was "sending a good signal overall for people to get through their study in a reasonable period of time".
Ms King said she thought the petition had obviously had some effect.
"I am just hopeful that Christmas is coming for them, because it has been a dampener on medical students, and it was a stupid decision when [Mr Joyce] made it and [it] wasn't based on any evidence.
"If he is going to announce it, get on with it so that students next year know exactly what they are facing."