Many Europeans cheered when Barack Obama was elected president. Disdain for his predecessor ran so high that, even in Britain, pollsters found that George W. Bush was considered a greater threat to peace than Kim Jong-il and Mahmoud Ahmadinejad. Only Osama bin Laden outpolled him.

But President Obama hasn't lived up to European expectations. The disillusionment is showing. French President Nicolas Sarkozy has characterized him as weak. And at a U.N. Security Council meeting on nonproliferation, Mr. Sarkozy chided Mr. Obama with the reminder that "We live in a real world, not a virtual world."

Many Europeans, of course, still cling to the notion that Mr. Obama is "one of us." And certainly no American president has been friendlier to the political values of Europe.

But to Europe's dismay, Mr. Obama can't find the time to attend this year's annual U.S.-European Union Summit - something Mr. Bush always managed to do. Mr. Obama's decision to skip the summit offended Europeans, who saw it as a deliberate snub of the European Union - their favorite project to centralize government and internationalize the governance of human affairs great and small. Given Mr. Obama's embrace of such ideas domestically, Europeans were understandably puzzled that he would not rush to link arms with them in the summit.

Further souring relations was Secretary of defense Robert M. Gates' blast at much of Europe for dithering on defense. At last month's meeting of NATO officials, Mr. Gates said the "pacification of Europe" (meaning Europe's turning away from war and defense spending as necessary policies to keep the peace) was making it difficult for the allies to "operate and fight together."

"The demilitarization of Europe," he argued, "where large swaths of the general public and political class are averse to military force and the risks that go with it, has gone from a blessing in the 20th century to an impediment to achieving real security and lasting peace in the 21st."

Mr. Gates is absolutely right, but put that aside for a moment. The in-your-face nature of his words is striking. No Bush administration official - not even Donald Rumsfeld - ever publicly criticized Europe's lack of military spending and support for NATO so bluntly. Europeans hammered Mr. Rumsfeld merely for suggesting there was a "new" and "old" Europe. Now we have a secretary of defense arguing that European fecklessness threatens world peace.

It is one thing to start a quarrel with France or even the EU, but Mr. Obama has managed even to offend the British. Many commentators in the UK now accuse Mr. Obama of harboring anti-British sentiments. The State Department's recent announcement that we would remain neutral in the Falklands Islands dispute between the UK and Argentina has only fueled that perception.

Daniel Hannan, a British member of the European Parliament and former fan of Mr. Obama's, put it this way in the London Telegraph: "Look, Mr. President, I was one of the few conservatives who truly wanted you to succeed. I didn't mind the way you snubbed our PM: I mean, most of us feel the same way about him. I didn't mind about the mildly anti-British passages in your book, or the boxed set of DVDs or the returning of the bust of [Winston] Churchill. But this is different. This is serious. How would you feel if, the next time you found yourself at war with some tyrant, we were simply to issue a terse statement saying 'our position remains one of neutrality'?"

Mr. Hannan's growing concern over Mr. Obama's policies is shared by many on the opposite side of the European political spectrum. With regard to the Obama presidency, illusions are shattering across Europe. There, as here, the left's exaggerated hatred of Mr. Bush was matched only by their naive embrace of Mr. Obama. They now increasingly realize that although Mr. Obama may admire Europe's domestic polices on health care and energy, he has little practical use for the European Union's pretensions to world influence and leadership.

But he does seem willing to give them precisely what they've requested for years: A diminished U.S. role in the world. Mr. Obama is pulling back on the projection of American power. Leaving the Europeans to their own devices (and ignoring their summits) is merely part of that program.

Their confusion is understandable. They expected that waning American power would mean less criticism from Washington and more European influence over U.S. policy. It didn't work out that way. Instead, administration officials are blasting European security policies in language that would make even Mr. Rumsfeld blush. On top of that, Mr. Obama was not even able to save Europe's favorite international agenda item - the climate change treaty in Copenhagen.

Europe may never get over its disdain for Mr. Bush. But they may someday come to realize that things were not as bad under Mr. Bush as they thought. At least he showed up to their meetings.

A former assistant secretary of state for international organizations, Kim R. Holmes, is a vice president at the Heritage Foundation and author of "Liberty's Best Hope: American Leadership for the 21st Century."