I think the first challenge for National should be to get Clem Simich made Speaker, instead of Margaret Wilson. Simich is well liked by most MPs and seen as scrupulously fair, so this is not an impossible task. However National needs to start pushing his candidacy before Labour signs minor parties up to agreements which include a requirement to vote for Labour’s nominee for Speaker.
Wilson will be guaranteed 51 votes from Labour/Progressive. And despite all their noble squeals about MMP and independence, the Greens will vote for a partisan Labour speaker over a neutral National one any day. So that is 57 votes.
National and presumably ACT will vote for Simich which is 51 votes. So the parties to target are NZ First, United Future and the Maori Party.
The fact Clem is technically part-Maori may help with the Maori Party. But the stronger argument to make to them, is that voting Simich for Speaker will be a perfect way of showing to their voters that they will not be Labour’s lapdogs. And a neutral Speaker will help them in the House as they ask questions to the Government. So if Maori Party on board that is 55 for Clem.
NZ First will probably need little encouragement to vote for Simich over Wilson, especially with the antipathy between Peters and Wilson. It also needs to be sold to them as a way to be seen as independent, despite voting to keep the Government in office on supply and confidence. So with NZ First you have 62 for Clem and 57 for Wilson.
If you get NZ First and Maori Party then you don’t need United Future. However would be best to talk to them at an early stage and try and persuade them to not include voting for Speaker in any support agreement with the Government. Labour need the minor parties more than they need Labour, so this should not be hard to achieve.
If Greens pick up a seat off National, and United Future did decide to vote for Wilson, you could have a 61:61 tie. In that case I would expect a deal to be done to have Simich made Speaker.