Chief Minister Andrew Barr and his deputy Simon Corbell, who now also has Burch's job of police minister, have been briefed by police, and say the matter goes beyond an indiscrete conversation with a powerful trade union leader. It is serious and warranted the resignations of a minster and her chief of staff, Barr says. It is unprecedented, Corbell adds.

Press further and ask, yes, but what exactly is the matter at hand?They won't say. Ask the police what, precisely, they are investigating? They won't say. Nor are the two people whose conversation provoked the crisis, chief of staff Maria Hawthorne and CFMEU boss Dean Hall, divulging precisely what was said.

But Hall's belief that his phone was bugged – a belief that Barr appears to accept – would at least explain how this has come to light. It appears that something was said that cemented pre-existing police concern about their dealings with Burch's office.

It is probably fair to say that the police have never been especially happy with the appointment of Burch as police minister. They are a conservative organisation, sticklers for process and not big on sharing information. From many accounts, Burch's office operates quite differently, sometimes sloppy on detail, ineffectual, indiscreet in this circumstance and with a tendency to take things personally and react vehemently to criticism.

No one, other than Hall, Hawthorne and anyone who has listened to or seen a transcript of a tape that might or might not exist, knows what was said. But few find it surprising that something might have been said that was indiscreet or unwise, that would upset the police or imply a breach of confidentiality, judgement or professionalism.

It's not clear what Corbell meant by saying the crisis is unprecedented, but it would be accurate to say it is unprecedentedly peculiar. If it is as serious as Barr insists – and a ministerial resignation in quick order backs the characterisation – why have the police not taken action already? The perhaps-covertly-recorded phone call was in April. If it is so serious, why did it take a media story to spark the week's chain of events? And if it is so serious, what is Barr doing announcing his minister's resignation by embargoed press release timed to coincide with the airing of a pre-recorded interview with the television networks? A crisis such as this demands a press conference where the chief minister stands up to explain what he can, and answer questions. So much of the week's events defy explanation.

It is an understatement to say the Burch crisis is one Barr does not need on the eve of an election year. He has a big enough fight on his hands to retain government as it is, with the loss of his deputy, opposition to the tram, ongoing upset over land prices and planning and the general unhappy odour that hangs about Labor's relationship with unions in the wake of the royal commission.Add to this the longevity factor, and the electorally unalarming face of his opponent Jeremy Hanson, only reinforced by the soft-left love affair with Malcolm Turnbull.

As one Labor insider put it this week, the government must be sick to the back teeth of starting each year with a controversy over Burch. Two years ago, it was the Hitler parody at the Fringe Festival, which saw journalist Lisa Cox pointing even then to a "lack of political shrewdness that has defined Burch's tenure in cabinet", not over the parody itself but the appointment of a controversial figure to run the Fringe without tender and Burch's inability to articulate her message convincingly.

She is not a good performer, nor does she appear to understand the professional relationships that are part of interactions between minister and media, and perhaps also between minister and stakeholder.

A year ago, it was her decision to rush through a change to allow $50 notes in poker machines on the eve of Christmas, a decision quickly reversed by Andrew Barr when it became public in January, who gave the minister a public telling off.

"It's not enough for the minister in that portfolio just to consult with the club industry," he told The Canberra Times. "I want a broader level of consultation and community engagement."

He was disappointed and concerned at her pre-emptive actions and had told her "that I expect a change in approach in terms of how the government engages with the community".

But within weeks she was embroiled in another controversy, this time over her son's volunteer appearances in schools with Menslink. Her son, while awaiting sentencing for armed robbery last year, was in schools without the required working with vulnerable people clearance, and his involvement in the program caused deep rifts in the organisation (and raised eyebrows about Burch's role as police minister). On that occasion, the Labor parliamentarians rallied around Burch, sharing her vociferous criticism of the media as intruding where it shouldn't on an issue involving her family.

Burch (and perhaps her parliamentary colleagues also) never understood the Menslink crisis as an issue of legitimate public scrutiny, despite retired Supreme Court judge Ken Crispin, the parliamentary standards commissioner, finding that it certainly was. While Crispin found that her advocacy on behalf of her son was not a breach of the ministerial code of conduct, it remains at the very least arguable that she showed lack of judgement in allowing her son to be in schools in the circumstances. The request of Menslink chief executive Martin Fisk to help her son and his willingness to accede also go to a lack of professional distance in community relationships.

The boy-in-a-cage affair looks to have been the final straw in Burch's relationship with the education union, which voted no confidence in her and has effectively stopped dealing with her. The union is upset over the way blame was laid at the feet of the school principal, insisting she was scapegoated, but concerns with the minister went deeper.

In May, education union ACT secretary Glenn Fowler said the sector "continually question the competence of the minister in administering her portfolio" and "consistently found the minster's ability to resolve ... matters sorely lacking". "There is utter confusion and the minister has taken to speaking in riddles," he said then.

The repeated criticism of Burch's performance has common themes – a lack of professionalism and judgement and an inability to properly separate the personal from the professional. It seems the police might hold similar concerns, or at least a distrust of how her office worked and whether confidential information could be trusted to remain confidential.

The influence of the CFMEU in Labor is another matter and one Barr would do well to tackle.

In April, former chief minister Jon Stanhope pointed to "the damage which is being done to the ALP by the concentration of power in the hands of a small coterie of union-based faction leaders".

Federal leader Bill Shorten should have welcomed the royal commission from the start, Stanhope said, and should have given "an unequivocal commitment of zero tolerance in the event any officials were found to be corrupt or where dodgy union practices were identified by the commission".

Two weeks ago, Shorten borrowed Stanhope's words when he announced "zero tolerance for criminality or corruption in the union movement" after the latest CFMEU arrest when two Victorian officials were charged with blackmail.

In the ACT, two CFMEU officials were charged with blackmail this year; one case is pending, the other has been dropped.

Union secretary Dean Hall hasn't been accused of any wrongdoing by the commission or anyone else. But it is a fascinating suspect of this week's events that if his phone calls were being listened into, it was presumably by police attached to the royal commission – which was Barr's interpretation when he said, "Obviously the leaking of a conversation though the royal commission processes has triggered a police investigation."

Hall has challenged the police to release that tape, insisting there was only ever one call with Hawthorne and his dealings with Burch's office were "benign". And you would have to assume that whatever was said it remained well within the bounds of the law, given that if there was anything of potential interest to the royal commission into union corruption said, it would be with commission investigators.

Hall might well have a legitimate beef with the way the police are interpreting right of entry laws on to work sites – which was the issue at hand when Burch took the union's concerns to the chief police officer. But his influence in the party is unarguable and it's not an easy political sell for Barr. This is the factional leader, remember, who was blamed for the dumping of Corbell, a leading light of policy ambition and innovation in the Barr government.

Corbell goes at the next election, resigning after he was dropped to an unwinnable spot in the left ticket by votes that party insiders insist are controlled by Hall and his factional cohort. It is difficult in that context to carry an argument that the union does not have excessive influence. But Barr rejects the assessment and apparently sees no need to distance the party from the CFMEU.

He does, however, look to be sending strong hints to Burch that it might be time to think about ending her political career – foreshadowing she might be dumped from the ministry altogether in the late January reshuffle.

With Mary Porter also retiring, with her departure date yet to be announced, and Corbell going at the election, Barr has a difficult juggling act in his ministerial reshuffle. Corbell is responsible for the big portfolios of health and light rail, along with renewables, attorney-general, and now police and emergency services, as well as being deputy chief minister. Barr won't want him to carry all of that into the election, given he isn't standing.

But with Burch sidelined, who is left? Just Yvette Berry, Mick Gentleman, who are both already in Cabinet, and Meegan Fitzharris and Chris Bourke on the backbench.

January looks certain to see a big promotion for Berry and Fitzharris becoming a minister. The rest remains a mystery.