He cannot afford too long to concentrate on the caucus beyond the leadership coup itself.
Decisions about his reshuffle will not unite a divided caucus but he has to be generous to minimise bitterness within the Bridges' camp.
He has already committed to keep finance spokesman Paul Goldsmith, who has been in the job for only a year, which will be good for stability.
He has to decide what to do with former deputy leader Paula Bennett, who has been replaced by Nikki Kaye. Ditching her as campaign chair would be destabilising if she were not willing to go.
Nikki Kaye in the fernery at Parliament. Photo / Mark Mitchell
And not least, Muller has to decide what to do about high-profile front-bencher Judith Collins.
One thing that will be puzzling many people is why Collins was not running for the leadership contest this time.
With the country on the verge of a severe economic recession, Ardern's greatest vulnerability is whether she has the background and strength to be the best leader for the times.
From that respect, Collins is certainly the clearest alternative to Ardern over Muller, and the one person who would have guaranteed an electric election campaign.
She has a national profile already.
Simon Bridges and Paul Goldsmith. Photo / Mark Mitchell
Her public persona is one of strength and no nonsense, although she has a softer side as well. She embodies both liberal and conservative traditions in the party, being a social liberal, but a conservative on law and order and economics.
She was a high-performing government minister and has perhaps been the most effective Opposition MP.
She is the closest the party has come to producing a Muldoon – someone who exudes authority and possibly relishes that fact a little too much.
No one would be left wondering what her values were or whether she had the experience to handle the job.
Collins has certainly made no secret of her leadership ambitions in the past.
She has had two previous bids for leader, against Bill English in 2016 and against Simon Bridges in 2017, and two bids for deputy leader, against Paula Bennett in 2016 and again against Bennett in 2017.
Judith Collins in her parliamentary office. Photo / Mark Mitchell
So where has she been?
The fact her previous forays have been so unsuccessful meant she has got to a point at which she is not going to enter another contest she is not assured of winning.
She does not want to be branded a perpetual loser.
Collins' ambitions rose to the fore again last year as the National Party grappled with two issues: a slump in support after the Christchurch massacre and its own internal debate over climate change policy which was being stirred along by Collins.
That is when Muller started assessing his chances.
He had just been promoted from Climate Change to Agriculture spokesman.
He was not going to challenge Bridges for the job but there was every likelihood if Collins had challenged for the leadership last year, he almost certainly would have joined a contest last year.
It also happened that Bridges and Muller were on the same side in the climate change debate.
The National Party caucus in 2018.
Attempts by Collins to drum up opposition to the Zero Carbon Bill were not successful in the broader agriculture sector or the caucus and she was seen as attempting to undermine Bridges.
Bridges was saved by the polls. The party's polling slump in mid-year had recovered within four months and the rationale for a Collins bid faded.
Collins has gained more support and more respect among her peers in this term of Parliament but not enough. And none of her supporters are heavy-hitters in the caucus.
She is more popular in the party and among the public than she is among her colleagues. She has had some influence over the outcome of this contest, however, and that is not to say her chance at leadership won't come – possibly soon.
The caucus has gambled on Todd Muller to try to claw back the gulf between Labour and National.
There is a very small chance of him becoming the next prime minister in four months' time.
If he fails miserably, it will be time for the caucus to go crawling to Judith Collins to beg her to become leader.
