What would Wendy Alexander be doing career-wise if she had not enjoyed the patronage of Gordon Brown? She once toyed with the idea of missionary work in Africa but it wasn't for her. Perhaps she would have gravitated towards academia, given the alleged size of her brain. Perhaps she may gravitate there still.

It is unlikely, though, that she would have made it as a politician without Brown's endorsement and all the credibility that has brought with it in Scotland. For she is lacking in the most basic political skills, as the events of the past week have demonstrated to anybody not already acquainted with her failings.

But for Brown, she would certainly never have dared to turn down cabinet jobs she deemed beneath her, nor run scared from one leadership contest (against Jack McConnell) only to return unopposed when the coast was clear six years later.

You could say she owes the prime minister a lot. But politics is a ruthless game and, when your poll ratings plummet and your immediate future looks bleak, it's each man (or woman) for himself.

So instead of sparing a thought for Brown's own precarious predicament following his disastrous local election results in England and Wales, Alexander decided to do something drastic. Taking her friend in No 10 completely by surprise, she announced she was going to support a referendum on independence, an abrupt U-turn on Labour policy.

She obviously reckoned that this was as good a time as any to assert her authority over the Scottish Labour party, but in one swift move she destroyed the unionist bloc in the Scottish parliament, the bulwark against advancing nationalism. Only afterwards, it appears, did she begin to consider what her actions meant. Surely if she had thought through the consequences, she would never have opened her mouth.

Her tactics left Brown horribly exposed at the dispatch box, pilloried by David Cameron as a leader who has lost control in his Scottish heartland. He has been forced to publicly contradict his Scottish protégée, though neither he nor she will acknowledge there is a split. Even more embarrassing, the Calman commission, which Brown has just set up to review Holyrood's powers (and to please Alexander), now looks redundant.

Calls for her head among senior Westminster Labour politicians have intensified, and she has been mocked as “a car crash” of a leader. She has wiped 10 years off Alex Salmond, who can't stop smiling; she has created what looks like an irreparable rift with the Scottish Tory leader Annabel Goldie, and has become a new target for the Lib Dems' barbs.

Yet such is her arrogance and her misreading of political realities that she believes the current row will blow over in a few days and the focus will then shift to the substance of the issue.

The Scottish people deserve a choice, she now claims, and the SNP's refusal to move forward its timetable for a referendum damages Scotland. She thinks she has pulled off a masterstroke, but her audacity is widely seen as stupidity.

Apart from the fact that parliamentary procedure prevents Labour tabling a referendum bill (how did she not know this?), she is an unpopular leader, 70 points behind Salmond in polls, and does not have the clout to bring off such a stunt.

She is not now and never has been backed by the Scottish public - and without Brown she will have even less standing - however much her loyal stalwarts plead on her behalf. Interestingly, it is the Labour men who are out there for her this time - Malcolm Chisholm, Iain Gray, Duncan McNeil, George Foulkes; what has happened to the women - Jackie Baillie, Pauline McNeill, Margaret Curran - who defended her previous unintentional wrongdoings so vocally?

Alexander's biggest blind spot is that she disregards the importance of courting support. With breathtaking cynicism she dismisses any opposition as ignorance. Everyone will come on board once they understand the merits of her argument. More than any other Scottish politician, she treats the electorate with utter contempt, is incapable of answering straight questions and is not above bare-faced betrayal.

If she wanted to challenge Brown, fearing that his potential defeat at the next general election would contaminate her, why not admit it? Why not say that her opinion on an independence referendum had moved away from the party line? Why add to the public's confusion, or does she not feel the need to explain herself?

It is difficult to see how Labour will restore its fortunes by backing a referendum. The SNP is popular, despite its independence agenda, as last year's election and recent polls have shown. Even a resounding “no” to separation is unlikely to dent Salmond's high approval ratings.

And what if he becomes more popular? Given that voters often put the personality before the politics, the Union could be in deep trouble. A tentative “no” or, heaven forbid, a “yes” would consign Labour to perpetual oblivion. None of this seems to have occurred to the Labour leader, who is prepared to gamble with Scotland's future in her desperation to remain in her job.

Through pig-headedness, she has placed not just her party and prime minister, but the Union in a perilous position. What was unthinkable a week ago now looks possible.

Salmond himself must admire the way in which she has catapulted constitutional matters to the fore of political debate, here and in Westminster. So much for tackling those bread-and-butter issues, Wendy. But who cares about health or education or social justice when you have a career crisis?

This column has called for Alexander's resignation before on grounds too numerous to mention. Of course she should go now but as she won't of her own accord she must be pushed. Brown is still her boss - she is only the leader of Scotland's Labour group at Holyrood - and he must act like it. As to who might take over the Labour party in Scotland, boost morale, rebuild its reputation with the electorate and rehabilitate it as a serious vehicle of opposition, I hear Coco the Clown is not very busy.