Stephan Shakespeare is a founder and global CEO of YouGov.

Voters are widely assumed to be stupid because they want contradictory things – for example, both more spending on public services and lower taxes. True, most people would rather like great-tasting ice cream with no calories, but it is not stupid to want contradictory things: it is stupid to believe you can really get them. The public doesn’t believe that. Overwhelmingly, it wants Britain to refuse paying the EU’s £1.7b surcharge, so David Cameron banging his fist is popular – but people confidently predict he will end up capitulating.

The Prime Minister has two electoral assets. Voters credit his Government with delivering an ok economic recovery; and they see him as being reasonably centrist and sensible. But they feel lukewarm about him. No, that’s an exaggeration, tepid is a more accurate word. Luckily for him, they are decidedly cool about Miliband.

Cameron, with his recent swing to a more anti-EU, anti-immigration stance, is leaning closer to what is desired by those voters he needs to keep him in Number 10, but he is simultaneously putting himself at risk of becoming less credible to them. They definitely want the zig, but they may not like the zag; polls have inched his way, but in the end he may become less believable. The Prime Minister has opened up a real vulnerability to Labour. So long as Miliband remains incapable of exploiting it, Cameron may remain safe; but it is a gamble.

Polling on Europe suggests people love to see it criticised, but are nervous about breaking away. In a referendum, I think it’s likely the nation will choose to stay in. Our most recent polling shows (as polls consistently show) that while people say they want to leave a Europe that fails to adapt, if they are offered any compromise at all – even the flimsiest, most transparent fig-leaf of a trivial concession – and they will vote to stay in. My assessment is that Britain would only vote to leave the EU if the Out campaign is vigorously led by a credible Prime Minister, which until recently has seemed highly unlikely.

This has become slightly less unlikely. Cameron may find he has manoeuvred himself into a position that he will find uncomfortable. During the past three months, I interviewed 21 chief executives of our top public companies for a YouGov-Cambridge study into attitudes to business. They were almost universally negative about Miliband, but among the ones I interviewed in the past month there was a notable rise in nervousness about the new direction of Cameron. As one of them expressed it to me: “This is Labour’s opportunity to work themselves back in with the business community.”