The heat is on the New Zealander after he led the team to a 4-1 defeat in Australia, with his England and Wales Cricket Board employers launching a formal review into the series within hours of the final Test concluding in Sydney.
The picture got even murkier when news emerged that Harry Brook, captain of the limited-overs side and Ben Stokes' deputy, had been fined for a late-night altercation with a club bouncer on the eve of a one-day international defeat in New Zealand before the team flew to Australia.
The entire regime is battling a growing perception of unprofessional preparation, loose training methods and a damaging drinking culture, leaving those in positions of power with difficult questions to answer.
McCullum revealed his own conversations have already begun with ECB chief executive Richard Gould and chair Richard Thompson, who were both in Sydney to watch the end of Ashes, but was less forthcoming on details.
Asked if he had spoken to the pair about his role, McCullum said: "Yeah, I have, but I'm not going to go into that. I'm not going to comment.
"I'm keen to carry on in the job, and we'll see. Ultimately, those decisions are up to them.
"Obviously, we haven't quite achieved the goal that we wanted to achieve by coming down here and winning but there has been some progress.
"You never want to throw out what's worked, you just want to keep chiselling away at some areas which need improvement.
"So I'd be loath to want to rip the script up and try and rediscover a completely different method."
England's next assignment is so close at hand - flying to Sri Lanka for a white-ball series in little over a week followed by the T20 World Cup next month - that McCullum is expected to lead it regardless of the ongoing review.
But it is now apparent that a detailed explanation of where the planning and execution of England's Ashes plans went wrong, combined with a clear prospectus for change in his set-up, will be needed.
Poor results, allied to the reams of unwanted headlines relating to the team's social habits in recent times, mean the status quo simply cannot hold. How far McCullum is willing to bend is less certain.
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