Yet he wrote the manifesto which catapulted them into government, every major piece of government legislation requires his sign-off, and he is the political figure whom Nick Clegg most trusts. Such power does not happen by accident.
On the one hand, he seems to talk sense: people are angry about the state of the economy. But then he'll suddenly claim the Lib Dems are poised to replace Labour as the lead force in progressive politics. It's mad, isn't it? But then, 18 months ago, anyone suggesting he'd be overseeing £700bn in government spending, would have been laughed out of town.
Suggesting even six months ago that the Lib Dem conference could require a venue larger than a phone box (once all its members quit when dreams of electoral reform were killed off) seemed fanciful.
So maybe, just maybe, Alexander is the sane one. Maybe all this business of "looking to the horizon" of the 2015 election, which seemed like an excuse for not taking too much notice of the latest grim opinion polls, is paying off. Maybe it really is all going according to plan.
"We are a party that can be relied upon on the economy," he says matter-of-factly, sitting forward on the leather armchair in his large Treasury office. A lot of what he says is a hard – maybe impossible – sell, but he ploughs on with impressive determination. It takes some chutzpah to telling Lib Dems booted out of town halls, or fearing for the impact of cuts on the most deprived, that they should be "very proud of the contribution" they are making to the Government's economic plan.
Despite losing 750 seats and control of nine councils in May, he says those who remain support what he is doing in slashing central government spending. Lib Dem councillors know what it's like to take over in places "ruined by Labour" and take some "bloody difficult decisions".
He repeatedly refers to the need to "sort out the mess" left by the last government. His attacks on Labour are so strong, it seems hard to believe he could work with the Miliband/Balls leadership in the event of another hung parliament. "I just think at the moment they are so utterly incredible, particularly on the economy."
He points out that Britain is not facing a sovereign debt crisis, and low interest rates are keeping thousands of people in their homes. Fairness in the tax system is key, he says. His announcement at today's conference of a new team of tax snoopers to hunt down the wealthy will please the Lib Dems. As if to rile those on the right of Conservative Party begging for the 50p tax rate to be jettisoned, he says he has "plenty of Conservatives saying to me" that they agree that raising the income tax threshold, a Lib Dem policy, is more important. Ditching the 50p rate would be "totally the wrong thing". He declines to say if pressure to ease the pain on the wealthy has come from Tory colleagues around the Cabinet table.
He repeats George Osborne's well-worn line about us "all being in it together" and says he works "very closely" and "very well" with the Chancellor. A little too well for some Lib Dems, who fear that Alexander, along with some Lib Dem ministerial colleagues, are too close to the Tories.
Some were appalled at the hard-line response of Conservatives, including the Prime Minister, to this summer's riots. But Alexander backs the idea of councils evicting rioters. "It's their own local decision to do that under extreme circumstances and yeah, I think it is right that councils have those powers but equally it's right that councils use them sparingly."
Those in the traditional social democrat wing of the party remain unhappy about doing a deal with the devils in the Tory party. However, Alexander, like Clegg, believes the Lib Dems have no future as a party of the left, though denies he is "on the right or the left ... it's about getting the job done". He quotes Russell Johnston, his predecessor as a Highlands Liberal MP, who said "liberal positioning in politics was like the nose in relation to the rest of the face: somewhere in the middle and out in front".
Yet voters gave the Lib Dems more than a bloody nose in May's local elections, and the prospect of the party being out in front any time soon seems unlikely. Alexander, though, takes heart from the experience in Scotland of his mentor Jim Wallace, when Lib Dems joined a coalition with Labour in 1999. "He and his colleagues were vilified for 18 months. As time went on, people saw what Liberal Democrats were doing. Gradually people's minds changed." (Four years later, the Lib Dems clung on to their 17 seats, but by this year slumped to just five. Not the best of omens.)
"I think we are going through something very similar, albeit in very difficult economic times," he insists. "We are having to make some difficult and, I know, painful decisions which I believe have to be done for the good of the country."
Yet there remains a perception that the pain is not being shared around fairly, that banks – and their high-rolling bankers – have got away scot-free, after taking the economy to the edge. The Vickers Commission appears to have been kicked into the long grass of 2019 and small businesses still complain about the lack of lending.
Alexander accepts that "people are angry" but is adamant that the £2.5bn levy on bank balance sheets and restructuring of the City would not have happened if Labour had remained in power. While help for business has been put in place – cutting corporation tax, extending business rate relief holidays and extra allowances for investment – he stresses that "for individuals I'm afraid we all have to make a contribution to this great national effort to sort out our finances". Hence the crackdown on tax evasion and avoidance.
There is still a feeling of "them and us", though. At the very top, pension pots are ballooning – up 70 per cent in the last decade for bosses of FTSE 100 companies. Alexander will not comment, saying it is up to shareholders to be "active in expressing their views". At the other end of the scale, proposals to reform public-sector pensions have become the catalyst for industrial action, with unions claiming it amounts to a pay cut for working longer.
Plans for a large-scale strike on 30 November, the day after the Treasury's autumn statement, are "very disappointing", but he makes clear that "good contingency plans" are being drawn up to limit their impact. "Whether you work in the public sector or the private sector, as we are living longer – and that's fantastic – that has to be shared between time in work and time in retirement. We can't all go on with ever higher pensions." He maintains that unions need to continue talks, and even after the changes that will increase contributions and delay retirement age public-sector workers will still get "among the best pensions available to anybody".
It all seems so straightforward. Three-quarters of the Lib Dem manifesto is being implemented, which is something "we need to shout about". A lot of it isn't, of course, such as its pledge to scrap tuition fees, which tore the party in half and led to effigies of Mr Clegg being burnt in the street. And the handling of reforms to the NHS has raised serious questions about the way the coalition works, and how Andrew Lansley, the Secretary of State for Health, could announce such a controversial package of measures which contradicted the coalition agreement.
Alexander admits that one of his jobs is to "have a close eye on the big policies in government". The Lansley plan was one of the first things in his ministerial red box when he joined the Treasury. As a member of the so-called Quad (with Clegg, Cameron and Osborne) he is supposed to stop policy cock-ups of this kind ever being made public. "I'm not sure I am going to kick over the traces on that one," he says defensively. Though he believes the government reaction, to pause the reforms and consult more widely, has earned them credit for listening. Every cloud, and all that.
In truth, any hopes of Lib Dem survival rest on the economy. Yet many pressures – from rising food and energy costs to global instability, including the euro – remain beyond the coalition's control.
As a spin-doctor for the Britain in Europe campaign in the late 1990s, Alexander was at the forefront of the pro-euro movement. The crisis sweeping through the eurozone has meant a harsh dose of reality for europhiles. Paddy Ashdown warned that the days of the euro as currently configured are numbered. Alexander disagrees, insisting no country will leave the single currency and that it will survive in its current form. "Look, I don't have a crystal ball any more than you do but yeah I do – I think that."
His confidence that everything will be OK will surely be tested as the cuts start biting and the economy wobbles. He may not have a crystal ball, and it is not certain that the Lib Dems will survive. But they just might.
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