Labour says the Ministry of Social Development was laying off IT staff at the same time as it was introducing self-service kiosks at Work & Income offices.
Security flaws at Work & Income computer kiosks allowed the downloading of 7000 documents, including medical and other details about children in state care.
Labour says MSD has cut IT staff numbers from 382 to 312 since 2008.
Social development spokesperson Jacinda Adern said the Work & Income kiosks were developed in-house by the ministry and introduced in 2010. Security flaws were found a year later, but not followed up.
She said the cuts, at a time when major projects were in development, raise big questions about whether staffing issues contributed to the privacy breach uncovered last week.
Ms Adern said a job can only been done properly when it is adequately resourced and the hacking suggests that is not currently the case at MSD.