Pulling U.S. troops out of what Obama once called a “dumb war” was one of his foremost campaign promises as a presidential candidate.

It comes on the heels of major breakthroughs in the administration’s foreign policy: the raid in May on Osama bin Laden’s compound that killed the world’s most wanted man, the death of al Qaeda militant Anwar al-Awlaki in September and subsequent drone attacks that have killed Taliban leaders.

While it wasn’t involved directly in Libya, the United States supported – and some argued initially led – NATO’s mission to aid Libyans rebelling against Gadhafi. Obama’s supporters say Thursday’s news was a vindication of the president’s strategy in that region, given that even Republicans such as Sen. John McCain, R-Ariz., and GOP candidate Mitt Romney have praised the president’s policy.

The long-term implications of Obama’s foreign policy, however, are not quite clear. With the tide of change turning rapidly in the Arab world, experts caution that it’s too soon to declare success on the international policy front.

“In strategy, the only thing that counts is the outcome,” said Tony Cordesman, a national security analyst at the Center for Strategic and International Studies and a former Defense Department official. “In Iraq so far, the outcome is largely negative. In Afghanistan, it’s very hard to say.

“We may be winning significant tactical victories, but it’s far from clear that the path we’re on is going to win the war” against terrorism.

The fear of increased Iranian influence in Iraq continues to dominate, while attacks by the Taliban and al Qaeda in Afghanistan and Pakistan continue to mount despite bin Laden’s death. In Libya, where some are calling for an investigation into how Gadhafi was killed, there are fears of a leadership vacuum and a surge in violence, similar to what Iraqis have experienced in the past nine years.

Arms and weapons have also flowed freely into Libya in recent months, experts say, which could have negative implications for the United States in the long-term.

“We also secretly supplied arms and so did the others - the Qataris and the Saudis in particular – and we didn’t know who the hell we were supplying arms to,” said Pulitzer Prize winner Leslie Gelb, now a senior fellow at the Council on Foreign Relations. “Now, of course, we are very worried about the arms, in particular we are very worried about the arms we sold to Gadhafi, which are quite sophisticated and a lot of them have ‘disappeared.’”

The United States remains deeply unpopular in the Arab world, which continues to pose a challenge for Obama.

“The Arabs, like people elsewhere, credit us with more power than we have,” Gelb said. “They dislike us because they believe Obama can wave the magic American wand and fix things. And that’s absurd. But that’s what Obama is up against.”

Domestically, Obama’s recent foreign policy successes have largely been met with bipartisan praise. But when it comes to an election boost, the events of recent months are unlikely to provide a significant one.

“Given the economy and given that international engagement generally is not very popular right now … he can’t really capitalize on this,” said Stephen Flanagan, Henry A. Kissinger chair at the Center for Strategic and International Studies.

Obama has also angered liberals by some of his foreign policy decisions, such as sending more troops to Afghanistan.