Until recently opinion polls had suggested a close run between opposing sides in a referendum on 22 issues relating to European policing and justice, at a time when the EU is facing huge divisions over how to deal with mass immigration and terrorism.

But in a Gallup poll published on Wednesday, the 'No' camp had a clear lead over 'Yes' advocates by 42 to 37 percent.

The number of undecided voters has apparently shrunk from about 30 to 14 percent, making the outcome more predictable than before.

The eurosceptic, anti-immigration Danish People's Party, the country's second most popular, has striven to portray the vote as a plebiscite on Europe.The DPP's posters adorn most lamp posts adjoining cycle lanes along which thousands of Danes commute. They declare simply 'No more EU.'

The DPP believes the Union's main foundations, the euro and the Schengen agreement, which permits free movement within the continental mainland, are fatally flawed, and that it would a grave error to further undermine the small Scandinavian nation's sovereignty, especially when so many other EU members are displaying self reliance and a lack of trust in Brussels by erecting border fences.

No more EU

The simplicity of the DPP's message is striking a chord, not least because the argument in favor is more complex and difficult to grasp.

Primarily, this is a vote about remaining a member of Europol, the pan continental agency that combats terrorism, organized crime, and people trafficking.

It also would commit Denmark to 'opting in' to 22 legal codes, covering such subjects as child pornography, cybercrime, human smuggling and fraud.

The minority center-right government of Prime Minister Lars Lokke Rasmussen is leading the ‘yes' campaign, and it has come under fire for phrasing the wording of the referendum in such a way that many people have been left confused.

The ‘Yes' camp has been accused of scaremongering by using posters such as one with a teddy bear, suggesting that Denmark would become a haven for paedophiles if it says 'no.'

After the "Islamic State" massacres in Paris killed 130 people, some security experts have been calling for a strengthening of Europol, to facilitate greater intelligence sharing.

Best for Danish interests?

The French attacks had been expected to boost the ‘yes' campaign. But so far, such a trend has not been reflected by opinion polls. Although it's worth noting that across Europe in the past year, in Britain, Greece and Denmark, pre-election surveys have been substantially wrong.

"The Danish government supports a yes in this referendum because we think it serves Denmark's interests bests to be closer associated with the EU," said Soren Pind, Justice Minister, during a television debate this week.

And Marcus Knuth, integration spokesman for the governing Venstre (Liberal) Party, said a yes vote would allow Denmark a better say on future EU directives. "A yes vote will ensure an opt-in model, which gives the Danish Parliament the ability to say yes or no to all future directives on legal matters from the EU. This is a unique option that few other countries have. Likewise, a yes vote will ensure that Denmark remains a full member of Europol, which is crucial to our ability to combat international crime," he told DW.

Meanwhile Morten Messerschmidt, the DPP's most prominent European parliamentarian, has been trying to convince voters that they should not worry about facing expulsion from Europol.

"Of course Denmark must remain in Europol. We have 18 months to negotiate a parallel deal because the current pact does not run out until 2017," he said.

It's unclear whether either of these opinions are making any headway when one newspaper described the referendum as one that makes the voters eyes glaze over.

But the outcome will be closely watched in Britain, which is due to hold its own referendum on EU membership in 2017.

A no vote will undoubtedly strengthen the eurosceptic camp in the United Kingdom, and could further weaken the European project.