President Barack Obama is clearly liked overseas — adored, in many quarters.

But is he respected?

Americans bathed in glowing press coverage of his trip evidently think so, judging by results in the latest CBS-New York Times poll. By 67 percent to 18 percent — including 45 percent of Republicans — respondents said they thought world leaders do respect Obama, though 52 percent still said that the United States is not respected.

Obama made himself popular partly by emphasizing as much as possible his differences from his utterly disliked predecessor, George W. Bush.

Even though every slight and slap at Bush was interpreted by some conservative commentators as Obama’s denigrating the United States itself, some of it was legitimate. And some of it was not.

At his town hall meeting in Strasbourg, France, Obama said that “in America, there’s a failure to appreciate Europe’s leading role. … There have been times where America has shown arrogance and been dismissive, even derisive.”

Well, he was puffing Europe’s “leading role,” but it’s true that, during Bush’s first term, arrogance, even derisiveness, was a common theme.

Defense Secretary Donald Rumsfeld and others gibed at “old Europe” and acted as though the United States — “the world’s only superpower” — could handle all the world’s problems alone and preferred to do so.

Obama did not give Bush credit for changing his tone in his second term, but that change was never noted by European publics, even though it was by a new generation of European leaders like France’s Nicolas Sarkozy and Germany’s Angela Merkel.

Obama was evenhanded in his chiding. He said, “In Europe, there is an anti-Americanism that is at once casual but can also be insidious. Instead of recognizing the good that America so often does in the world, there have been times where Europeans choose to blame America for much of what’s bad.”

Where Obama was needlessly (if only implicitly) negative toward Bush was in Istanbul, Turkey, where he said that “the United States is not and will never be at war with Islam.” The truth is that it never was, as Bush said again and again.

Conservative critics have tried to brand the Obama administration’s dropping the term “global war on terror” as an abandonment of the war on terror itself, but that’s not fair, either.

Obama clearly has dedicated himself to fighting terrorists — and he calls them that — with a huge new commitment of money, troops and civilian aid workers to Afghanistan and Pakistan.

He has also committed American prestige and has taken political risk to do so.

In the CBS poll, only 39 percent of respondents — 33 percent of Democrats — said they favor the increased troop commitment, and 33 percent opposed it.

To merit the world’s respect, Obama’s effort to neutralize Al Qaeda and the Taliban in Afghanistan and Pakistan has to show progress. He’s doing the right thing in pledging $1.5 billion in U.S. aid to Pakistan and trying to get other nations to provide more.

But it’s not a good sign that NATO allies did not answer his call for more troops for Afghanistan. They will provide 5,000 trainers, but no more combat forces.

Nor did Europeans — especially Merkel and Sarkozy — go along with Obama’s request to pump up economic stimulus to fight the global recession.

The G-20 summit did agree to an increase in funding for the International Monetary Fund to help emerging economies, including Eastern Europe, but that was not a contested issue. In fact, it relieved the European Union from the burden.

Obama and Russian President Dmitri Medvedev agreed to restart strategic arms-reduction talks — more a Russian priority than an American one — but Obama got nowhere in persuading the Russians to join in stopping Iran’s nuclear program.

Russia’s price for such an effort will be Obama’s cessation of plans to deploy anti-missile sites in Poland and the Czech Republic. Obama seems prepared to pay that first, after which he will have to hope that Russia plays its part in the bargain.

It will be a major test for Obama whether he can stop Iran from developing nuclear weapons. If he can, without Israel taking military action first, then Obama truly will deserve and get respect.

He is starting out simultaneously playing good and bad cop with Iran — saying it will not be allowed to develop nukes and also promising direct diplomacy.

The Iranians have shown no sign that they will ever stop their nuclear program, so it’s likely Obama will have to impose stiffer sanctions, possibly cutting off Iran’s gasoline imports. Can he persuade other countries to go along?

While he was overseas, North Korea fired off an intercontinental ballistic missile. Prior to that, Obama declared that, referring to U.N. resolutions against Pyongyang, “rules must be binding. Violations must be punished. Words must mean something.”

But North Korea went ahead. And the U.N. Security Council did nothing because the United States could not persuade China or Russia to impose sanctions, or even make a menacing statement. That’s not a good sign of respect.

And on the heels of the North Korean launch — and a successful Iranian satellite launch in February, meaning it has its own ICBM — the administration announced that it was cutting missile defense by $1.4 billion.

Obama said again and again on his trip — correctly enough — that the problems of the 21st century cannot be solved by military power alone, but require international cooperation.

That’s music to much of the world’s ears. But while world leaders want an American president who listens to them, too much humility could mean not enough U.S. leadership.

The test for Obama is whether he can get Europe, Russia, China and other powers to join him in facing the world’s mortal dangers. So far, the jury is very much out.

(Morton Kondracke is executive editor of Roll Call, the newspaper of Capitol Hill.)