On Wednesday, the German Finance Minister Wolfgang Schaeuble is due to meet the U.K. Chancellor George Osborne to discuss the payment.
The European Commission, the executive arm of the EU, made its initial demand last week after reviewing the economic performance of each of the EU's 28 member states since 1995. Its new calculation showed that the U.K. has grown more than previously thought over recent years and so it has asked it to contribute more the budget.
On Tuesday, the EU said Britain's budget rebate was at risk if it did not cough up the money by the deadline. Cameron has stuck to his guns, telling parliament on Monday, "We're not paying 2 billion euros on the first of December and we're not paying ... a sum anything like that."
In spite of the mounting hostility to the EU among large sections of his governing Conservative Party and the U.K. in general, the Prime Minister may not have much of a choice.
"The real question is how much he is going to end up paying," Robert Oxley, Campaign Director of Business for Britain, told CNBC Europe's "Squawk Box" on Wednesday.
"Tory backbenchers [members of parliament with no government office] have set a limit of about £400 million, anything more and David Cameron is going to be in trouble to make the case to the British people that remaining within the EU with such a large bill is the right choice for Britain."
Read more: Britain's growth slows as row over EU bill flares
Against a backdrop of rising anger towards perceived meddling in UK affairs by the EU, David Cameron has attempted to soothe public anger by saying he will renegotiate the terms of the U.K.'s EU membership. He has also promised a referendum on EU membership should his Conservative party win another term in power in the general election next year.
The EU's decision to make the demand at such a politically sensitive point in EU-UK relations was "politically inept," according to one analyst.
"Someone's political radar really should have been on at the Commission," Pawel Swidlicki, Research Analyst at independent think tank Open Europe told CNBC on Wednesday. "It's no good to pretend it's merely a technocratic measure as this can't be divorced from domestic politics."
The U.K. is not alone in being asked for more money with the Netherlands, Italy, Greece and Cyprus also being asked to stump up more cash. In contrast, France, Germany and Denmark are among countries getting a rebate.
Read more: Why forgiveness could be France's best bet
Britain shouldn't make the payment before "checking that the figures are right," Richard Corbett, Labour MEP for Yorkshire and Humber, told European Squawkbox. "[Britain shouldn't pay the bill] without first checking whether it's right to make the calculation of Britain's underpayment going back so many years and if it does have to be paid whether it can't be spread out over a number of years."
He believed, however, that a referendum to leave the EU when the U.K.'s priority was to see maintain its economic recovery would be "a bit odd."
"The real question is how we change Europe and improve the European Union, not the false choice of staying in or going out when leaving would be economic suicide."
- By CNBC's Holly Ellyatt, follow her on Twitter @HollyEllyatt.