ACC Minister Nick Smith says no decision has been made on when the ACC reform bill will be introduced to Parliament despite the Government now having the numbers.
The Injury Prevention, Rehabilitation and Compensation Amendment Bill contains cuts to a range of entitlements and pushes out the deadline for fully funding ACC.
The Maori Party on Tuesday agreed to support the bill's first reading, despite having several concerns about the legislation.
A Radio New Zealand political reporter says that support extends only to the first vote on the legislation, which would send it to a select committee for public submissions.
Prime Minister John Key says the Government is looking to the longer term and would not want to see the bill stranded at committee level.
He says talks are ongoing with the ACT Party, which wants the Government to open ACC's workplace coverage to private insurers.
Maori Party co-leader Tariana Turia says her party has concerns about the idea, but is willing to investigate its potential.
Analysis by the Treasury into the opening up of ACC's work account to competition suggests that there may be net gains from increasing contestability in claims management.
The Prime Minister sought input from the Treasury and released its findings on Wednesday.
Mr Key says the Government has not undertaken any serious analysis of introducing competition into the work account.
He says while the Treasury's document does list some advantages to contestability, it also outlines disadvantages.
The Treasury says the economic gains may be relatively modest in the short term because ACC's problems are predominantly in other accounts.