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Officials are warning of the consequences of failing to approve a budget.

“Let there be no mistake: the absence of an agreement would be harmful for all of us,” Mr. Van Rompuy wrote Tuesday.

Already the Germans are hinting that foot-dragging may be the least harmful solution.

“If necessary, we will have to meet again at the beginning of next year,” German Chancellor Angela Merkel told her parliament on Wednesday.

If there is no deal up to 2014, there would be a rollover of the 2013 budget plus a 2 percent increase accounting for inflation.

At the heart of the budget fight are the conflicting vantage points of rich EU countries and poor.

Wealthy nations such as Germany, Britain, Sweden and the Netherlands are becoming increasingly tired of bailing out countries such as Greece and Spain, which feasted on EU development funds before collapsing under piles of debt.

At the same time, up to 15 poorer nations are exhorting them to continue funding projects to close the wealth gap between the mostly northern and western nations and the southern and eastern members.

The European Commission, the EU’s executive, backs more spending, arguing that cross-border initiatives on everything from science to pipelines will help to create the economic growth and jobs that the bloc of a half-billion people needs.

Hundreds of EU Commission staff gathered outside EU headquarters on Wednesday to protest possible cuts, and trade unions called for a half-day strike to boost their demands.

Mr. Cameron has made cuts among EU staff, which are derisively called Eurocrats in Britain, a key part of his demands.