Repeat after me: don’t get your hopes up. Not just about the prospects of Donald Trump getting hammered in the US midterms, difficult as that is to resist, but about the accuracy of polls that just happen to coincide with your heart’s wildest desire. The smart response to Survation’s mega-poll for Channel 4 suggesting Britain would vote by 54% to 46% to remain if we had another Brexit referendum tomorrow is almost certainly to note that polls are notoriously fallible; that remain was ahead going into the last referendum and a fat lot of good that did them; that remainers still don’t really seem to understand the country they live in. Beware the tyranny of hope, and all that.

But “what if … ?” remains one of the most destabilising questions in politics, because it niggles away at the ground beneath one’s feet. What if something has changed? What if the one thing we thought we knew for sure – that the people had spoken, so there was at least a clear mandate for delivering what they wanted even if what they wanted was practically impossible to deliver – is no longer sure?

It’s a particularly awkward question for Labour frontbenchers, so many of whom are currently enabling something both they and the party membership think is a lousy idea in the interests of not losing the next election. The biggest shift Survation found was in predominantly Labour areas in the north that voted heavily leave in 2016, although admittedly many of those representing these communities aren’t feeling it on the doorsteps. “Please stop telling me what my constituents think,” the Darlington MP Jenny Chapman tweeted recently, when her colleague Chuka Umunna cited a separate poll commissioned for People’s Vote suggesting every Labour seat now backs a second referendum. “They can and do speak for themselves.”

But this is also an acutely difficult moment for MPs representing remain seats, whose constituents are increasingly exasperated with their failure to resist and rebel. It’s one thing reluctantly going along with something against your better judgment. Going along with it against the electorate’s hastily revised judgment would be the sort of cataclysmic failure of leadership for which the Labour party won’t easily be forgiven. What if, what if, what if?

But this poll won’t make entirely easy reading in Downing Street either. Theresa May now seems close to doing a soft-ish Brexit deal leaving open the option of Britain staying in the customs union if (as seems likely) it has no better answer to the Irish border problem. The idea that enthusiasm for Brexit might be waning could strengthen her hand against colleagues who see this deal as a watered-down travesty, ensuring she ends up with something less likely to unleash chaos and closer to her own instincts.

But it’s unhelpful, to put it mildly, that the Survation poll also shows nearly half of voters don’t much seem to care what happens to Northern Ireland. There is a worrying divide emerging between Westminster, where the sanctity of the union and of a peace process that has saved so many lives is rightly uppermost in minds, and an electorate seemingly not that bothered – at least right up until the consequences of it become real to them, when they’re arguably quite capable of deciding that isn’t what they wanted after all.

The will of the people is so often presented as a cast-iron certainty, a compass needle any idiot could follow if they weren’t so blinkered by their own arrogance. But maybe what the age of populism is showing us is that it’s actually a much more fluid, flickering thing. Maybe the truth is that actually people change their minds all the time, although sometimes only to change them back again; that all polls can really capture is a snapshot of opinions that not unreasonably change when the facts do, and in the end there’s no escape from politicians exercising judgment. It’s impossible to know for sure whether the public mood has shifted, let alone whether it’s shifted decisively enough to justify a second referendum. But after two years of struggling to square a practically impossible circle, all sides must now at least confront the possibility of voters not really wanting a square any more. What if, what if, what if? It’s not the immovable certainties in life that keep politicians awake at night. It’s that tiny, niggling sliver of doubt.

• Gaby Hinsliff is a Guardian columnist