The SNP canvassers are baffled. “We don’t understand what’s happening. Nobody does.” If the consistent polls are believable, Scotland’s voters are preparing to give the Scottish National party a towering majority on 7 May, mostly at the expense of Labour. But why? And what do they mean by it?

In Kirkcaldy, part of Gordon Brown’s old constituency, the SNP candidate for Westminster is Roger Mullin. He’s a university teacher, with long political experience. But he is astonished by what he finds. “Every day we are supposed to fill in returns about the issues raised on the doorsteps. But people just aren’t raising issues in the usual general election way. Instead, they want to talk about bigger stuff: the SNP itself, Nicola Sturgeon, a hung parliament in London.”

His team agree. Like canvassers in several other constituencies, they say it doesn’t feel like a normal parliamentary election. But neither is it a rerun of the 2014 independence referendum: they are emphatic about that. Oddly enough, that campaign did get the public pushing forward issues: people all over the country were eager to offer policy proposals about: “What sort of Scotland?” The election south of the border has its unusual features, but basically it’s the same old two giants slugging it out over tax-cut costings or nurse numbers. It doesn’t carry the Scottish sense of new process, of a powerful glacier of opinion broadening and scooping up bits of old landscape as it finds its way to an unknown destination.

It’s difficult to take the polls quite at their face value, with their suggestion that Labour in Scotland would be scythed down to single figures. The fact that 30% of the Scottish samples have not yet made up their minds and even the ancient warning against peaking too soon – all that qualifies prediction. And yet no scepticism removes the prospect of an SNP breakthrough on 7 May.

What is this glacier made of and where is it coming from? As everyone now knows, the defeat of the yes campaign in the 2014 referendum was followed by a surge in SNP membership, the party almost quintupling its membership in a few months. Some of these joiners were people, many of them previous Labour supporters, who fancied independence but didn’t fancy the SNP or, in particular, Alex Salmond (who resigned as party leader after the referendum result). But it now looks as if they have joined their opposites: voters who felt the SNP was good for Scotland but who thought independence was “mebbe naw” – a step too far or too soon – and may well have voted no in the referendum.

This helps to explain another curiosity: the lack of abuse towards SNP canvassers. They get the usual earful from Tory and now Ukip punters, both rare on the ground. But men and women who open the door and firmly declare themselves for Labour are often surprisingly polite.

Their traditional combativeness isn’t there. It could be they are in shock after reading the polls. But it may also be they sense the convergence that is so obvious to outsiders. The grassroot visions of Labour and SNP supporters about the sort of society they want to live in only diverge in detail.

So if this political movement, this “glacier”, is not primarily about either independence or roads, schools and hospitals – what is it about? Nationalism, certainly, but which kind? Those doorstep concerns in Kirkcaldy give some sort of hint: “The party itself, Nicola, a hung parliament.” This is Scotland saying with a new intensity that it no longer feels part of “the Westminster system”. Does that amount to not feeling part of Britain?

Not yet I think. Sturgeon’s line is that Westminster is still reformable; it might be worth staying there for a bit longer. There she may be taking a risk. Public opinion, morbidly sensitive to media insults and threats from Down South and convinced that all London “vows” will be broken, may grow restless as she tries to modernise Commons procedures or intervene in English school financing.

Nobody knew any of this was going to happen. A serious conversation about Scottish elections a year ago would have assumed that the nation was moving into a dual-loyalty pattern. At Holyrood elections, the SNP might well go on being the party of majority choice, but at Westminster elections the voters would return to Labour as the traditional party for resisting the Tories.

That, roughly, is how it looked after the shock of the 2011 Scottish elections, when Salmond and the SNP won an absolute majority at Holyrood. Labour, to its disbelief and rage, lost a string of seats, not so much because its vote didn’t hold up but because the Lib-Dem vote collapsed towards the Nationalists. But only the year before, Scottish Labour had done fine at the Westminster elections. The notion of one party for Edinburgh, the other party for London, seemed logical and sophisticated.

But it was superficial. Labour’s 2011 defeat, especially in old working-class areas, had shattered its confidence, as gathering doubts among its supporters about Iraq, Blairism and New Labour’s social policies came to the surface. Simultaneously, the SNP completed its transit to the moderate left, while its government record, even as a minority administration between 2007 and 2011, was judged “quite good”.

In the longer term, social change had undermined the Labour hegemony. The party’s generations of self-sacrificing struggle to win decent housing, the council schemes in which most people lived, were forgotten, while the movement’s base in the labour forces of heavy industry and mining had almost vanished in the 1980s. To the college-educated young whose fathers might have worked at Scott-Lithgow’s shipyard, Clydebank shipyard or down the Lady Victoria pit – vanished industries – these struggles were irrelevant.

Looking back down the years, it’s probably true that Scottish Labour in the 1970s had a chance to saddle the colt of reviving nationalism. But the party, once in favour of Scottish “home rule”, missed the opportunity. By the mid-20th century, its leadership was rigidly committed to socialism through one central Labour government.

The Scottish trade union movement came to support devolution long before Harold Wilson, ironically enough, sent a team up from London in 1974 to batter the party comrades into accepting that a minimal dose of self-rule was not the path to fascism. But it was not until Tony Blair’s time that the party accepted the idea of a Scottish parliament with anything like enthusiasm.

For the last 50 years, the SNP has begged the public to accept it as “Scotland’s party” – the only party to have no strings attaching it to London, free to concern itself exclusively with Scotland’s interests. While the SNP remained on the margins, the claim was taken with a pinch of salt: they would say that, wouldn’t they? It’s a different story today. Whether they want independence or not, substantial numbers of the Scottish electorate are now ready to buy Sturgeon’s assertion that the SNP is “the party of Scotland”.

This, then, is what the thousands who have joined the SNP or intend to vote for it are trying to say. Whatever it may lead to, the big movement we are watching is developing into the affirmation of one political party’s right to speak for the Scottish nation, with a legitimacy no other grouping can attain. Sturgeon has helped to bring this about.

Her public performance in the seven months since the referendum has been extraordinary. Even those who dislike her policies can’t help feeling proud of this “wee cracker” who has made the world listen to Scotland.

But there are perils. Hubris, first of all: SNP popularity up to now has alternated between dizzy surges and long slumps. Second, there wlll be tension between taking an active part in how Britain is governed and the heavy swing in Scottish opinion against the whole Westminster system. Third, the small party that keeps a bigger one in power may find that it has become the big fellow’s prisoner, not its master. A combination of those problems felled the Irish parliamentary party 100 years ago.

And in the distance gapes an elephant trap – the “Quebec Syndrome”. An independence movement wins a grand majority as “our party” of Quebec or Scotland: people agree that nobody else can represent them. But when that movement holds an independence referendum – its basic raison d’etre – the same people draw back: too big a step into the unknown. The party gets over its defeat and is re-elected with most of the same enthusiasm – and holds another “indyref”, which also narrowly fails. For a nationalist movement, this is the beginning of a spiral into disintegration and despair.

Will Sturgeon’s SNP fall into that spiral? Her view of independence is instrumental: it’s the means to social justice and prosperity, not the end in itself. That’s what allows so many Scottish socialists to vote for her. So in this perspective her party could succeed for a long time by remaining in the UK and advancing Scotland’s interests in the House of Commons. Independence would arrive in its own time: no need to rush after it.

It may be too late for that. I used to think Scottish constitutional wishes were basically unchanging: “We want to govern ourselves as other small nations do. Within the UK if it’s possible, but if not, then through independence.” I believe that was true for the last 50 years. But now, as this glacier creeps over old landscapes, I am not so sure. Soon the roads to Westminster will be under the ice and the new Scottish generations will not know where they ran.