WASHINGTON (AP) ― The dramatic advance of Libyan rebels over the forces of longtime strongman Moammar Gadhafi offers vindication, at least for now, for President Barack Obama’s decision to refrain from using U.S. troops on Libyan soil and to let NATO take the lead.

But the chaotic scene on the streets of Tripoli Tuesday illustrated the uncertain path to stability and the hazards that still face the White House.

How Libya moves away from the current turmoil will present the next challenge for Obama and could determine how the public views not only his foreign policy, but in some measure the U.S. economy as well. Underscoring the volatility, Gadhafi’s whereabouts remained a mystery, fighting between rebels and Gadhafi loyalists continued, and oil prices remained in flux.

Still, the news for Obama could not have been much better. The Libyan street was euphoric, rebels overran Gadhafi’s main military compound and hope grew that over time the price of oil ― a contributor to dangerous economic lethargy ― would dip.

“The Libyan intervention demonstrates what the international community can achieve when we stand together as one,” Obama said at his vacation retreat in Martha’s Vineyard, Massachusetts.

Obama was careful to emphasize that uncertainty remained and that Gadhafi’s regime could still pose a threat.

Obama called French President Nicolas Sarkozy to talk about the situation in Libya, among other things. They agreed to continue to work with allies and partners to protect the people of Libya and to support a peaceful transition to democracy.

It will take several months even under a stabilized Libya before its oil fields are producing enough crude to start exporting again. But any extra shipments could lower the price of gasoline, which has already come down more than 40 cents a gallon (10 cents a liter) from its peak in May.

Back in March, Obama gambled that the way to confront a potential civilian catastrophe in Libya was to build a coalition of NATO and Arab countries to use airpower ostensibly to protect Libyan citizens from a Gadhafi crackdown. But his intent was clear all along: Gadhafi had to go.

The Libyan leader was deemed a sponsor of terrorism, and his regime in 1986 was found responsible for bombing a Berlin discotheque frequented by U.S. troops. Three people died in the explosion. Two years later, a Libyan agent planted a bomb that blew up Pan Am Flight 103 over Lockerbie, Scotland.

The uprising in Libya follows the death of Osama bin Laden at the hands of U.S. special operations troops, a major achievement for the Obama administration and one that solidified the president’s standing with the public on his handling of terrorism.

But Gadhafi’s removal has additional implications. A stabilized Libya would mean the country’s oil production could go back online, potentially reducing the cost of oil, which spiked globally in February as the flow of oil from Libya dried to a trickle.

Time and again, the president has cited the uprisings in the Arab world and the increased cost of oil as “headwinds” that have imperiled the economic recovery.

Libya has the largest oil reserves in Africa. Before the uprising, it was the world’s 12th largest exporter, delivering more than 1.5 million barrels per day mostly to European markets.

The news of the rebels’ success was affecting Brent crude, which is used to price many international oil varieties, dropping 92 cents to $107.70 per barrel in London on Monday. It rose back up to $109.44 Tuesday as the strength of the dollar weakened against the euro and other currencies.

“If oil prices continue to head south, that’s a real plus for the economy,” said Mark Zandi, chief economist at Moody’s Analytics. “We can take all the plusses we can get at this point.”

So could Obama. While the president’s overall approval with the public is above 40 percent in most polls, the number that approve of his handling of the economy dropped to a new low of 26 percent in a Gallup poll last week. By contrast, 53 percent approved of his handling of terrorism.