National Party leader Simon Bridges' stance has softened somewhat from his initial statement that the current law was his preference.
He now thinks there is room for modernisation and is open to removing it from the Crimes Act, but wants to see what Little puts forward.
"Anyone who has lived a little and had friends from all walks of life knows that things happen. There is complexity in life. But I would be very loathe to have late-term abortions at will, without checks and balances and medical input."
He is leaning towards the same option Little prefers but made it clear he wants Labour to carry the can for any backlash.
"Where the Government is putting it up I do think it's for them to make the case so we can assess it."
He warned the Prime Minister that reform "fatigue" could set in.
"A bit of friendly advice for the Prime Minister – New Zealanders may well have fatigue when it comes to all these chunky, yes serious, issues but complex ones when we are also trying to focus on the future direction of New Zealand come election time."
He expected there would be a wide range of views in National.
They include Judith Collins who has questioned the need for any reform, saying at 13,000 abortions a year, women did not seem to have a problem getting one. She also said it was not something that was raised by the public.
Amy Adams said she had tried to put abortion reform on the agenda when National was in government but it was ruled out. She was now keen to see reform happen and also favours the option Little does.
Those Labour MPs who supported reform were split between an option that gave women the final decision however far along a pregnancy was and the option Little supports.
Little said Cabinet will decide on a process before Christmas, and draft legislation was likely by early next year. The process would determine whether he consulted with other parties prior to putting legislation forward or simply put up a bill and then consulted as part of that process.
It was possible a dedicated select committee would be set up for it, rather than adding it to the Justice or Health Select Committee because of the public interest and large number of submissions expected.
He said that could mean legislation had passed by the end of 2019.
"Society's expectations have changed about how this issue should be managed and how individual women should be able to deal with this issue. In the end there will be a public debate about it and Parliament, MPs, they will decide whether there are enough of them for there to be a change in the law.
"I think the political ground has shifted in the last 10-15 years."
He believed there was a growing acceptance for taking abortion out of the Crimes Act.
While he believed a separate process was needed for later pregnancies, he did not believe it was a major issue in New Zealand given it was so rare.
It could also mean wider reforms.
"The report acknowledges that some of the delay in getting an abortion is because they have to go through these extra hoops. And an abortion that might have been carried out in the first trimester is pushed out to week 16, 17, 18."
WHERE THEY STAND
National Party leader Simon Bridges: Open to taking it out of Crimes Act, wants controls around late-term abortions.
Act Party leader David Seymour: Wants reforms, women should decide however far through a pregnancy is.
Green Party co-leader Marama Davidson: reform, Green Party caucus has to discuss best option but her long-held view was that pregnant people could be trusted to make decisions with the right support.
Justice Minister Andrew Little: reform, women decide unless pregnancy is more than 22 weeks.