But as leaders from across Europe gather in Brussels on Thursday to haggle over more than a trillion dollars in spending over a seven-year period starting in 2014, widespread public anger over perceived extravagance when national governments are slashing their own budgets has helped fuel a mood of hostility toward the world’s most ambitious and, until the debt crisis exploded three years ago, most successful experiment in economic and political integration.

This is particularly the case in Britain, where Prime Minister David Cameron, under pressure from implacably “Euroskeptic” politicians in his own Conservative Party, this week accused the union of “picking the pockets” of Britons. He has threatened to veto any new budget that does not at least freeze spending, and he indicated his support for a referendum that would give Britons a chance to decide whether their country should pull out of the bloc altogether. Such a dramatic and disruptive rupture, still unlikely but no longer unthinkable, has sharply raised the stakes in this week’s budget negotiations between leaders.

But it is not just Britain that has its hackles up. Across much of Europe, views of the union and its Brussels administrative apparatus have soured. Eurobarometer, the public opinion monitoring arm of the European Commission, found in a survey conducted in May that “Europeans who are attached to the European Union are now in a minority.” Fifty-two percent of those surveyed said they felt little or no attachment, up seven percentage points since 2010. In Britain, only 27 percent felt attached to the union.

Brussels officials acknowledge that they have an image problem, but they mostly dismiss it as a result of “misperceptions” of waste and exaggerated reports of bureaucratic red tape. Only 6 percent of all spending goes to the union’s administrative machinery, staffed by 55,000 people, including 6,000 translators, mostly in Brussels. Draft budgets under consideration this week propose a 1 percent reduction in administrative costs. Britain wants deeper cuts, arguing that the costs, while small, are symbolically important.

Ahead of this week’s negotiations, at least seven countries, mostly those that contribute more to Europe’s coffers than they get back in farm subsidies and other payments, have already warned that they may veto a budget that does not give them a better deal. Among these is Austria, where, according to Mr. Ehrenhauser, who sits on the European Parliament’s budgetary control committee, “there is a critical mass building against the European Union.”