Mr Nash said other police IT projects were more than six months late, and that suggested something was going wrong with the agency's technology and programme management.
Mr Bush denied there was an issue, and said the payroll overhaul was a very challenging and complex piece of work. Any cost increase would be met from within existing police baseline.
The Treasury is monitoring the HRMIS as part of its work overseeing the Government's 38 riskiest projects, which together total $20.5 billion.
In December, it released a report that rated the project as "amber/red", meaning delivery against its original budget of $56.2 million budget was in doubt.
Green Party police spokesman David Clendon said the budget blow-out was concerning, given the money would come from within existing baselines.
"It is concerning that technology, computer upgrades will take away money that people would otherwise expect to be spent on law enforcement."
The police payroll system is the latest Government IT project to experience problems. The Education Ministry's Novopay payroll system led to widespread pay errors for school staff. Eventually taken over by the Government, it cost an extra $45 million.
Technical changes to implement child support reforms also cost tens of millions of dollars more than originally estimated, while efforts to merge the computer systems of Customs and the Ministry for Primary Industries are almost $30 million over the initial budget.
