The Attorney-General says he's looking at whether it will be possible to hold an urgent select committee hearing for the bill on covert police surveillance.
The Government has put forward the Video Camera Surveillance Bill in response to a Supreme Court ruling that the use of hidden cameras in the operation that culminated in the 2007 Urewera police raids was illegal.
On Wednesday, Attorney-General Chris Finlayson sent a draft of the legislation to all parties and various legal groups.
The National-led government has United Future on board, but needs at least three more votes to pass the legislation before the House rises for the November election.
Labour says the bill is rushed and fundamentally flawed, far broader in scope than expected and would allow the police to use covert filming without obtaining a search warrant.
Labour leader Phil Goff says his party would vote for the bill's first reading only if the Government agrees to a select committee hearing.
He also wants provisions on covert surveillance - part of the Search and Surveillance Bill that was examined closely by MPs last year - to be picked up and included in this new legislation.
"Take that power and put it in the new legislation - don't pretend that you need urgency on this legislation," he told Morning Report.
The ACT party has said that if it was to support the bill any further than a first reading, an urgent select committee hearing would have to be held and the committee would have to approve the legislation.
Mr Finlayson said he is looking at the possibility of having a very truncated select committee hearing before Parliament rises and says he can see a way to take the legislation forward, despite the urgency involved.
"If parties engage with me and with the officials, as I've suggested, and with the police, there's a way through this without harming public safety."
The Attorney-General's office says nothing in the bill gives police any more power to trespass or enter private property without a warrant.
The Mana Party leader and its sole MP, Hone Harawira, has ruled out voting for the bill saying it is yet another piece of legislation with Maori in its sights.
More details on covert filming cases revealed
The Government wants to change the law so that footage already gathered by the police is not compromised by the ruling.
The police have provided details of the types of cases affected.
They say the types of investigations that involve undercover surveillance include murders, serious drug offending and violence, gang-related activity, and sexual offending including offences against children.
The Government says 40 court cases and 50 ongoing investigations involve undercover surveillance, numbers which have been questioned by defence lawyers who say covert techniques are rarely used.
The figures cited by the Government have now been confirmed by the police and Crown Solicitors.