However, the Government could scuttle his chances by making its own moves to toughen the rules for rental properties to keep its support partners onside. It is understood the Government is considering changes, possibly as part of the Budget, which will go some way to covering the proposals in Mr Little's Healthy Homes Guarantee Bill.
Mr Little's bill would set minimum standards for insulation, heating and ventilation in every rental property. It will have its first reading tomorrow afternoon. The private member's bill goes further than current Government proposals for rental housing, which focus more narrowly on insulation and smoke alarms and cover fewer properties.
Housing Minister Nick Smith has previously said Mr Little's bill would force extra costs on to landlords, potentially reducing the rental stock. But it now appears the Government could be prepared to make minor changes to proposed rental standards to satisfy its support partners.
It is not yet known whether Mr Little's bill will pass its first hurdle tomorrow.
United Future leader Peter Dunne holds the deciding vote. He could vote against it if he is satisfied with the Government's proposed changes to its own regime for rental properties. Mr Dunne previously voted in favour of a near-identical bill to Mr Little's - drafted by Labour MP Phil Twyford - which fell short by one vote in March 2015.
New Zealand First has gained a seat since Mr Twyford's bill was debated, meaning that if all parties repeated their support for Mr Little's bill it would pass.
The Government's legislation, which is before Parliament, will require rental properties with no insulation to upgrade to 2008 building standards. Rentals which already have insulation will have to upgrade to a lower standard.
Mr Little said the legislation does not go far enough.
"One of the big problems is the mould that's arising in people's houses and indeed houses that are just cold," he said. "Just having insulation isn't enough. You have to have a source of heating and then to prevent mould it's got to be properly ventilated ..."
Analysis by the Ministry of Business, Innovation and Employment shows that a comprehensive minimum standard for rental housing - which is broader than both National and Labour's proposals - would cost an average of $1800 per property. It would have a net benefit of $334 million, or $1.50 for every $1 invested.
The savings to the health, energy and social sectors could change, depending on the enforcement regime. If a warrant of fitness regime was used, the cost-benefit would fall to 88c for every $1 invested, the MBIE report said.
