National says it will not support a Green Party proposal to give domestic violence victims up to 10 days' paid leave from work, but the bill could still have the numbers to progress.
Labour and Act say they will back Green MP Jan Logie's private member's bill at its first hurdle.
The Maori Party is also likely to support it, though its MPs have some concerns about whether victims' privacy could be breached if they applied for leave because they had been abused.
New Zealand First and United Future are yet to confirm their position, but their support would mean the bill had the required 61 votes to pass its first step.
The bill was scheduled to come before Parliament on Wednesday but its first reading has now been delayed until March 8.
It has received votes of support from the Human Rights Commission, and Business New Zealand says it is worth further consideration.
Prime Minister Bill English said today his party was not supporting the bill. There was nothing to prevent employers from offering specialised leave to domestic violence victims, he said.
"Employers have that opportunity, some will take it. I would hope that employers are understanding and compassionate where they need to be with victims."
The Warehouse, ANZ, and Countdown already had domestic violence policies, as do some Government agencies including the Government Communications and Security Bureau (GCSB).
Workplace Relations Minister Woodhouse said he was sympathetic to the aims of Logie's Domestic Violence Leave Bill.
However, introducing an extra ten days of leave would have significant costs attached to it, Woodhouse said.
Logie said giving victims more protection in the workplace was "critical" to reducing the effects of abuse. A secure job gave victims domestic and financial stability, and a path to rebuilding their lives, she said.
Asked about the Maori Party's concerns about privacy, Logie said: "Workplaces should be identifying domestic violence as a workplace hazard, and putting policies in place to protect victims and privacy, in terms of disclosure, should be one of those policies."