As the vote in September nears, the argument about Scottish independence is naturally becoming more tense. And so, as the stakes get higher, is the argument about what the Scottish independence opinion polls are currently saying. To read some nationalist propaganda, you might think that the buoyant yes campaign is already neck-and-neck with the no campaign and about to take the lead. Alex Salmond played shamelessly to that mood in his weekend speech to the SNP in Aberdeen. But more objective judges remain significantly more cautious, pointing out that the no campaign remains ahead in every poll in Scotland, even those trumpeted by the SNP, while many of those polls still show a large lead for no, with some suggesting that the yes campaign may have lost a little momentum lately.

What cannot be denied, however, is that the yes campaign has had significantly the better of the first quarter of 2014. Last autumn, there was little movement in the polls. The expectation that Scotland would vote no remained solid, with nothing seriously to challenge it. Since then, however, two things have happened. First, supporters of Scotland remaining in the UK took up some big issues – on the currency in particular, but also about the European Union and, most recently, about the impact of a no vote on global stability. Second, those arguments had an impact on public opinion. But it was not the impact their advocates had hoped for. Ever since George Osborne went to Scotland in February and argued against a future currency union, it is the yes campaign that has prospered more.

The scale of that shift is very much disputed. So are the implications for polling day. But the reality of the shift should not be doubted. It is no longer possible to say with near-certainty, as it was as recently as the new year, what the result in September will be. Scottish opinion has moved towards the yes campaign. It may or may not move further in that direction between now and polling day. But the possibility that Scotland will indeed vote for independence is now a real one, and should be treated as such. The old complacency, not just in London but more widely, that the no campaign would win, is simply no longer valid. That's what foreign observers are telling their governments, as we reported last week. Now domestic opinion needs to catch up. The Scottish independence question cannot safely be ignored in favour of "bigger" issues – like the 2015 election, economic recovery and the UK's place in the EU. If Scotland votes yes, as it may do, all those issues will look very different. It's time to get more real about what is at stake.

The SNP came to Aberdeen for the final political conference before the referendum vote in very confident mood. They have momentum. They have organisation. They have emotion. And they have Mr Salmond. The first minister's speech was long on rhetoric. His sneery tone is not to all tastes. And Mr Salmond does not have the majority either. But he does have a strategy. He frames the whole independence argument as a proud Scotland's chance to break free from Margaret Thatcher and her heirs, including timid Labour heirs. There is a lot of wishful thinking there, but a message that things can be different is naturally a seductive one.

It is important not to exaggerate the shift in the polls, though many do so. The shift is partial, not decisive. But it is important to understand and learn from it, partly in order to make a better case for the continuation of the union, not just in Scotland. The no campaign has been right to point to the risks for Scotland and Britain from independence. Risks exist. To dismiss this as bullying is trite, part of the effort to frame everything as Scotland versus the Tories, but the fact that the charge resonates cannot be ignored. The no campaign undoubtedly also needs to make a more positive case for the values, benefits and shared sympathies that unite the people of these islands. The more its campaign can articulate what we have in common, and how it can be at the heart of a better Britain, the better.