Many of the MPs believed Muller's own supporters had been leaking about caucus discontent against Bridges for two years before one last frenzy of leaking amid the Covid-19 lockdowns.
Perhaps they considered the end justified the means, but a "rise by the leak, die by the leak" sentiment was inevitable among MPs who were offended by that.
If an investigation does take place, Muller may want to be aware of the perils of asking a question to which he does not already know the answer.
His predecessors can tell him such investigations inevitably come up empty-handed or with just a suspicion or, god forbid, an own goal.
It is certainly not the best way to start doing what Muller said he would do: talk about the things that actually matter to voters.
On that latter metric, Muller has so far failed miserably and has only himself to blame.
After a dream run over the weekend and the string of "getting to know you" media appearances, reality hit on Tuesday when normal political life resumed.
The trouble was that having pitched himself as a better salesman of National's positions than Bridges, he turned up with absolutely nothing to sell.
Thus far, he has ended up talking more about the dearth of high-ranked Māori and Pacific candidates in his shadow Cabinet and his political souvenirs more than the Covid-19 recovery.
Nor can he get away with only talking about Covid-19. Voters like to know a lot about a potential Prime Minister - the values they hold that will drive their decision-making, and where they stand on issues that affect their lives. A lot of this election will be about Covid-19, but not all.
The MAGA cap was a fireworks issue. It flared brightly, but not for very long.
The "white" front bench could plague him a bit longer because every photo of his team standing behind him will remind people of it.
The low placement of Māori and Pacific Island MPs seemed to be more by oversight than design.
That is almost as unforgivable in the 2020s - even in the National Party, which has long abhorred the suggestion of ethnicity or gender quotas, but has recognised the importance of Māori representation in its caucus.
A shadow Cabinet custom-built for the Covid-19 recovery does not mean all other considerations should be put to one side.
There was also the unfortunate mix-up over Paul Goldsmith, who was pointed to as Māori only for Goldsmith to say he was not.
Instead, his great-great-grandfather had two Ngāti Porou wives and two Pākehā wives and fathered 16 children. Goldsmith is descended from a Pākehā wife.
Muller's other defence was to point to Paula Bennett, his top-ranked Māori MP teetering on the end of his front bench at 13.
It is understood Muller had originally told Bennett she would have no portfolios, and no ranking at all – effectively a message to leave altogether.
He backed down on Sunday, clearly having been reminded that nobody puts Bennett in a corner.
Bennett is a popular figure in some quarters of the National Party, an experienced campaigner, and knows the party inside out. She more than anyone can help calm those in caucus who are upset about the way the change happened.
She is also Māori and so his reluctant decision to keep her on paid dividends almost immediately.
It was Bennett who came to his defence after his day of stumbles, saying on RNZ it was a very tough job and while Muller had had a rough day, she was certain he was up to it. It was a classier move than Gerry Brownlee's subsequent reference to "Simon's supporters" leaking.
On the Covid-19 topic that Muller had wanted to talk about, Muller's main argument so far has been that National had a track record in handling economic recovery.
In response to that, Prime Minister Jacinda Ardern and Grant Robertson have started highlighting that the track record was at the hands of John Key and Bill English: both of whom were gone.
Nor does it help Muller that Labour has actually offered up something by way of an economic recovery plan for Covid-19 – a $50 billion plan.
Muller, on the other hand, is yet to do so. He has promised it will come "and it will take New Zealanders by storm".
But it means he has nothing to talk about in the meantime.
Many have pointed out that those who rise to Leader of the Opposition do not realise how hard it is until they get there.
The media has some appreciation of that. After all, it is the media's willingness to give leaks a good home that help make the job so hard.
It requires a thick skin, fast-thinking, and some slow thought as well: thought about what and how to shape the policies that should shape New Zealand. It requires a disciplined caucus.
Most of all, it requires stamina and vigour.
The only person we have heard about who has shown any real evidence of that this week was Paul Goldsmith's great-great-grandfather, Charles Goldsmith, with his four wives and 16 children.
