If you believe the opinion polls, only complacency on an epic scale could harm the campaign to preserve the Union.

Those inclined to say No would have to stay at home in herds and droves next September just to give supporters of independence the chance of an honourable defeat. So say the polls.

If that's the case, what's eating the two Alistairs, Darling and Carmichael, respectively chairman of Better Together and the Secretary of State for Scotland? Rarely a day passes when they do not pause from ridiculing the Yes campaign to insert a squib into the posterior of Unionism. Whatever the polls suggest, these gentlemen aren't buying it.

In September, the former chancellor said that no-one could "possibly call the result of the referendum at the moment". As Mr Darling explained: "I don't want people who share my view to think 'I don't want to bother, the result's in the bag'. It's not."

This week, the Scottish Secretary has been sticking to the script. Talking to a London newspaper, he said he had been attempting to "put the fear of God" into a Coalition Cabinet liable to take polls for granted. Mr Carmichael even quantified his fears: "I am convinced that this is a fight that can still be lost … Winning with a 49-51 split actually resolves nothing. Do not assume we will get the 51% - we could end up with the 49%".

There is an art to managing expectations in a political campaign. The two men, public faces of Unionism, could be bluffing outrageously, or they could be telling the plain truth. They could be mindful of that unforeseen SNP election victory in 2011, or they could be working to ensure the Yes campaign is crushed utterly next September. It could be, quite simply, that they know better than to trust polls at this point in the battle.

Mr Carmichael, with his 49-51 split, certainly presents himself as that sort of sceptic. The polling pointing in the direction he mentions has been scant and derided by Unionists. But the Scottish Secretary is more interested in - and more worried by - the numbers of people who have yet to pick a side in this fight. Perhaps one in four voters have still to decide between Yes and No. If there is a big turn-out next September they will settle the issue.

Unionists are a little spooked by that thought, for several reasons. First, as Mr Darling said in September: "A nationalist who fervently believes in nationalism is going to be at the polling station at five to seven in the morning, and is guaranteed to turn out". The accurate inference was that those inclined to No, complacent or otherwise, are not so committed. It is hard to get excited over the status quo.

Equally, there is the fact that Yes have been campaigning among the undecided for a while. Their evidence, anecdotal or not, says people are more likely to shift towards independence than move in the other direction. In contrast, Better Together have been slow off the mark, happier with the dismal politics of rapid media "rebuttal" and daft melodrama - the separatist threat to Doctor Who, anyone? - than with those elusive positive arguments.

Then, for rejectionists, there is the biggest problem of all. Who are these undecided people, in the main? The answer was never a big secret, but Mr Carmichael has arrived at his own conclusions. Those are not liable to gladden coalition hearts. If the Scottish Secretary is right, and if - if - there is a big turn-out next September, Better Together have more of a scrap on their hands than blithe Unionists bargained for.

Mr Carmichael told The Guardian this week: "See how many undecided people there are. They are formerly reliable Labour-voting males in the urban post-industrial belt of Scotland. That is Glasgow, Fife, Lanarkshire, Ayrshire. They have a folk memory. They remember Margaret Thatcher and the de-industrialisation of Scotland in the 1980s. They were not overly impressed by 13 years of Labour government and as a result their loyalty to Labour has loosened. They went lock, stock and barrel to the Nationalists in 2011".

The Scottish Secretary isn't wrong. This column has argued before that the contest will be settled in what I still know, part-accurately, as the schemes, in those places Labour once used to take for granted and win on risible turn-outs. Glasgow and its hinterlands, as Mr Carmichael rightly says, will hold the key to the referendum. But if that is true, and if Yes can get the vote out, Better Together have more than complacency to worry about.

The Tory part of that coalition remains, as the fashionable jargon would have it, toxic. The Scottish Secretary's party is if anything worse off. Both parties are capable of losing more votes than they ever gain. To what extent, then, has loyalty to Labour "loosened"? Much more than its Westminster leadership comprehends.

We know as much from the divergent voting patterns of UK and Scottish elections. Labour still gets the nod, in terms of seats, when representatives have to be sent off to London. But when decisions have to be made in Scotland over Scotland's future, things change dramatically. A great deal of the old loyalty has evaporated.

So will this "formerly reliable" Labour constituency make itself felt next year? A straight answer to that question could help you take a bundle from the bookies. There has been talk of turn-out reaching 90% in the referendum. That would count as an actually historic achievement, no matter who came out on top. If it happens, as many as a million previously disregarded votes would be in play. Mr Carmichael says these people "have not been reached by conventional politics". That's one way of describing the abject failure of the parties to persuade a million people that voting is worth the bother. But how does a campaign dedicated to the system that bred failed parties persuade a million sceptics to turn out for the status quo? "Vote for more of what you despise" seems an unlikely slogan set beside "Vote for the chance of something new".

But let's apply a few brakes. People who don't vote have heard plenty of promises. What party fails to offer a bright new tomorrow? This section of the electorate lost its illusions, if it had any to begin with, a long time ago. It might well regard the word "historic" as just another label on the snake-oil bottle. You can deplore the attitude all you like, but it is born of experience.

Still, we know this much: the leading voices in Better Together regard the polls as worthless. They see a battle ahead on ground that neither Labour nor its coalition partners would have chosen. The task for the independence campaign, in contrast, is plain enough: to preoccupy the schemes in cities, towns and villages with the promise inherent in two words, Yes Scotland.

Messrs Carmichael and Darling have an equal and opposite task: to speak on behalf of mistrusted parties while breathing life into a dismal phrase. They have to do nothing less than persuade people who hate politicians that No, Scotland is an idea worth having.