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.