It is famously tricky to predict the outcome of referendums, which is one reason political leaders never call them if they can possibly avoid it.

As former French President Nicolas Sarkozy is said to have warned David Cameron when the U.K. prime minister was dithering over whether to give the British public a vote on remaining a member of the European Union: The government chooses what question to ask, but voters decide what question to answer.

In the end, Mr. Cameron felt he had no choice but to ignore Mr. Sarkozy’s advice, fearing his Conservative Party was under such electoral pressure from the anti-EU UK Independence Party that if he resisted a referendum, he might soon be out of a job. Now the time for that referendum is fast approaching: Following a summit of EU leaders last week, Mr. Cameron declared himself confident that he would soon secure a promised package of changes to the terms of Britain’s membership, paving the way for the great question to be finally settled next year.

The conventional wisdom is that the referendum is on a knife’s edge, with some polls showing the electorate evenly divided. Despite Mr. Cameron’s confidence that he can secure a satisfactory deal, anti-EU campaigners gleefully point out that nothing he is likely to do will reduce the flow of EU citizens coming to work in the U.K., which polls show is the issue that matters most to voters. Meanwhile, supporters of EU membership worry that Mr. Cameron has already had his most eye-catching demand—that the U.K. be allowed to deny tax credits to EU citizens until they have been residents for four years—rebuffed and that his failure will overshadow their campaign.

Even so, several things have become clear in recent weeks to suggest the conventional wisdom may be wrong. First, it is now apparent—if it were ever in doubt—that Mr. Cameron will campaign for continued EU membership whatever the outcome of his negotiations. Although officially he is keeping his options open, all his efforts are focused on keeping Britain in the EU; no official time is spent preparing for an exit. Even if Mr. Cameron was tempted to lead the “leave” campaign in an attempt to hold his party together, he has made too many statements emphasizing the importance of EU membership to Britain’s national security and economic prosperity to be able to do so without damaging his credibility. Indeed, voters might be so repelled by such naked cynicism that at this stage his support might hinder rather than help the “leave” campaign.

Second, Mr. Cameron may face less political resistance than commonly supposed. Euroskeptics are demanding that government ministers be allowed to campaign for an EU exit. But Mr. Cameron secured full government backing for his negotiation strategy, so any minister who wishes to challenge his handling of it now should expect to have to resign. It is possible that one or two marginal figures might quit, but leading party figures know that if they defy Mr. Cameron and the anti-EU campaign loses, their political careers will surely be over.

And if the anti-EU campaign can’t recruit senior cabinet-level defectors, it is hard to see many of Mr. Cameron’s backbench colleagues sacrificing their own careers to the cause.

Third, the anti-EU campaign is in disarray, despite the apparent hardening of the polls in their favor. Indeed, there aren’t one but two campaigns, and there are deep divisions—personal and political—between them. Their challenge is to persuade the British public that the status quo is intolerable and that they have a better alternative.

Yet, they can’t agree among themselves what Britain’s future would look like outside the EU, whether it would seek to retain membership of the EU’s single market and would therefore continue to be subject to EU rules, including the right of EU citizens to live and work in the U.K.; or if not, what form of new relationship they would seek and how they would persuade 27 other EU countries each with veto rights to agree.

Fourth, what is perceived to be the euroskeptics’ strongest argument may yet prove their weakest.

There is no doubt that the migration crisis and terror threat have combined in the public mind into a simplistic narrative of EU incompetence from which the U.K.’s only hope of protecting itself is to leave.

But in reality, the recent crises prove the opposite: that Europe is facing profound common security challenges that demand a common response—whether in looking for ways to stabilize Syria, Libya and Ukraine; adopting a common policy toward Russia and Turkey; securing the EU’s external borders; adopting and enforcing common standards on the treatment of refugees; or working together to address the cross-border terrorist threats.

Sure, pro-EU campaigners can’t be complacent: Mr. Sarkozy’s warning resonates. But surprises can go either way.

The final point is that the British referendum is another variant on the same political contest being played out across Europe, which Marine Le Pen, leader of France’s right-wing National Front, has accurately characterized as one between globalizers and nationalists.

British euroskeptics may not like to think of themselves as kindred spirits with Ms. Le Pen, but they are appealing to the same political constituency. And what all recent European elections have shown—including last week’s French regional elections where the National Front failed to win a single contest—is that while this constituency of those who feel threatened by globalization is large enough to present a potent political challenge, it has nowhere yet proved large enough to win.