'Crucial' 24 hours ahead for UK-EU reform deal

It's close to crunch time for the U.K and its future in the European Union.

U.K. Prime Minister David Cameron and the head of the European Council Donald Tusk are due to meet on Monday for further talks on the U.K.'s demands for EU reforms.

Cameron and Tusk met on Sunday for talks on the U.K.'s membership of the 28-country political and economic bloc but failed to reach a deal on three of the four key demands from the U.K. regarding immigration, sovereignty, boosting competitiveness and ensuring the protection of the single market for the U.K. and other non-euro countries.

Toby Melville - WPA Pool/Getty Images

Facing an increasingly powerful euro-skeptic group of parties and lawmakers at home, Cameron has been pushing hard for reforms in how the 28-country EU is run.

Securing the reforms are vital for Cameron: If he gets a deal, he has a stronger argument for staying in Europe in the U.K.'s referendum on membership slated for sometime this year. If he fails, the euro-skeptic camp can claim that the EU is beyond reform and the U.K. is better off out of the bloc.

On Sunday, a source told the BBC there had been a "breakthrough on restricting benefits for EU migrants coming to Britain but Tusk tweeted that "intensive work" would be needed during the extended talks.

There are hopes in the British government that a deal satisfying the U.K.'s demands for reforms and a renegotiation of its membership can be found ahead of a planned EU summit on February 18-19.

With an extra 24 hours of talks ahead, European Council President Tusk said that if there was progress in the talks, he would table his draft proposal to other European leaders ahead of the summit.

The referendum comes amid a tide of rising euro-skepticism in Britain, with polls suggesting a close result of the referendum a so-called "Brexit" is a distinct possibility although most analysts believe that "no" vote (a "no" to leaving the EU) will prevail.

Mujtaba Rahman, Europe practice head at Eurasia Group said in note ahead of the weekend's talks that the political risk research and consulting firm's base case scenario was for Cameron to secure a deal over his EU renegotiation at the upcoming 18-19 February meeting.

"In turn, this would pave the way for a referendum in June," Rahman said. The group believed that even if there was deadlock at the February summit, a deal could be reached in March, still allowing for a June referendum.

Eurasia's Rahman believed that the British public "will ultimately opt to stay in the European Union (EU), although we do recognize the risks that exist (our "Brexit" probability is around 30 percent)."

Other analysts are not so sure that euroskeptic Brits be convinced to change their expected voting intentions, even if Cameron manages to persuade other European leaders to concede to the U.K.'s demands for reforms.

Carsten Brzeski, chief economist at ING-DiBa, said that while there was little appetite in the EU to see Britain leave the union, the British public could be harder to convince that it's worth staying.

"The European Summit in February will be another attempt to accommodate David Cameron's demands and ideas (even if they are not entirely clear to everyone) on economic governance, competitiveness and sovereignty. In the area of immigration, the refugee influx could have made it easier for David Cameron to reach some kind of compromise with the European partners," he said in a note on Friday.

"Despite the fact that a compromise – at least in theory – is still feasible, it is very hard to tell where the negotiations exactly stand at the current juncture," Brzeski added, saying that the EU would do well to consider what impact a "Brexit" could have.

"As these negotiations are highly technical, it is hard to see how any result – even if presented as a victory for David Cameron – can be so compelling to the British people that they would lose their EU-scepticism…The rest of the European Union, therefore, is well advised to think of the unthinkable and prepare for a "Brexit."

Follow CNBC International on Twitter and Facebook.