The time frame was given in a briefing paper delivered to Mr Joyce last week and leaked since. It estimated 18 to 24 months "if we do nothing to change the users' experience".
Mr Joyce said he received the briefing paper just after getting the Novopay job and doing nothing was not an option.
He said a technical review of the Novopay system was due to report back in four weeks and would then allow a time frame for solutions to be fixed.
The review was being carried out by Deloitte New Zealand chairman Murray Jack, who was also heading the Ministerial Inquiry into the payroll disaster with Sir Maarten Wevers, the former chief executive of the Department of Prime Minister and Cabinet.
"Until that is done I can't give a reasonable estimate as to how long remediation will take."
Mr Joyce said the problems would "get sorted one way or the other". However, he added: "I'm reasonably confident we'll stay with the current system."
Four years' development went into the Novopay system after Australian recruitment company Talent2 won the contract in 2008. It was rolled out two years late and riddled with problems.
The problems were compounded by the need for schools to do 90 per cent of their payroll online but problems with the system meant it had peaked about 70 per cent.
The briefing told Mr Joyce there were too many errors at the Talent2 Pay Centre and the ministry had bolstered the company's staff with data entry operators.
The briefing also warned Mr Joyce that Talent2 had "no senior management bandwidth" in New Zealand. It stated the lack of senior executives affected the company's ability to make decisions about putting money into bolstering the service and improving it in the future.
Education staff hit by Novopay problems today can call 0800 663 772 or email resourcing@minedu.govt.nz with "manual payment" in the subject line.
Inside info
Are you working in a Novopay service centre? We want to know what it is like on the inside. Email: david.fisher@nzherald.co.nz
