Correction: An earlier version of this article about the NATO mission in Libya incorrectly said that the U.S. House passed a measure to reject U.S. participation. The House rejected a measure to authorize U.S. involvement. This version has been corrected.

As NATO bombs began to rain on Libya in March, President Obama and other Western leaders assured their war-weary publics that the campaign to protect civilians from Moammar Gaddafi’s crackdown would be over within weeks.

Now the coalition’s springtime incursion has stretched to summer, and Gaddafi’s resilience has startled the leaders who committed to the operation. Calls are growing to end it even as NATO pleads for more time.

As the campaign enters its fourth month, NATO officials insist that it is succeeding and that Gaddafi will become the Arab Spring’s third casualty. But that will happen, they say, only in a slow and steady advance on the capital as his troops run out of supplies, not in a flash of pyrotechnics that puts him out of power in an instant.

“The noose is tightening around him, and there’s very few places for him to go,” Gen. Charles Bouchard, the Canadian head of the operations, said Saturday in an interview at his Naples headquarters. But, he added, “You don’t stay in power for 41 years and expect that he’s going to leave at the first sign of stresses.”

Indications of a fraying commitment to the mission were evident in a House vote Friday in which an unusual coalition of anti-war Democrats and tea party Republicans joined to reject a measure to authorize U.S. involvement in the Libya operation, even as they declined to strip part of its funding. In Britain, a top commander said last week that if the campaign goes on past September, his forces could crack under the strain. On Wednesday, Italy’s foreign minister called for an immediate end to hostilities.

NATO has flown more than 4,700 strike sorties, pummeling bunkers, depots and vehicles and reducing much of Gaddafi’s army to ruins. It watches his military movements with drones that can remain in the sky for days.

Still, Gaddafi holds on, continuing to cause casualties in the rebel-held city of Misurata, in the mountain towns south of Tripoli and along the front line in the east.

Bouchard said NATO’s extreme caution about civilian deaths — in one case scuttling days of planning because a soccer game was being played next to a target — has slowed the campaign. The upshot, he said, is that there has been only one instance in which NATO thinks it may have caused civilian casualties, and few opportunities for the Libyan government to present evidence of more.

Both sides say that credible allegations of civilian deaths probably are the best weapon Libya can use against NATO. The nervousness was palpable at NATO’s operational headquarters on Friday before major strikes on Brega, a now-depopulated city near the main front line that NATO says government troops have been using as a base.

NATO later said it hit seven command-and-control nodes in the city, along with 28 other targets. Libyan officials said Saturday that the strikes killed 15 civilians, but they did not present evidence to support that number and in the past have exaggerated when saying that civilians were killed in strikes.

Measures that could speed Gaddafi’s departure, such as cutting overland fuel lines to Tripoli, aren’t being carried out because the United Nations mandate does not allow targeting civilian infrastructure, Bouchard said, adding that he is cautious about potentially harming civilians in the process.

One major problem with the campaign has been unrealistic expectations from the outset, analysts said.

“With any use of air power comes this public expectation that airplanes will prove our resolve, that we’ll be able to deter the enemy, that they can’t possibly win and will capitulate,” said Tami Davis Biddle, a military historian at the U.S. Army War College. “But this idea that aerial bombardment equals capitulation is a really flawed equation.”

Rebels have blamed NATO for their inability to make meaningful headway in their advance toward Tripoli, although they also say they are slowly smuggling weapons into the capital to undermine it from within. Rebel leaders based in the east say their grip on the besieged port city of Misurata — the bloodiest and arguably most important front line in the conflict — is fraying. Rebels took control of the city in late April, despite intense shelling and artillery attacks by forces loyal to Gaddafi, but they have been unable to push westward.

Rebel spokesman Mohamed Ali said opposition leaders are mystified by what they perceive as the coalition’s reluctance to more forcefully attack Gaddafi troops on the front lines.

“NATO is a mystery to us,” Ali, who is based in Doha, Qatar, said in an interview via Skype. “This is getting to a stage where it’s getting very, very dangerous.”

NATO officials say they are doing all they can without risking civilian casualties, pointing to Libyan government forces switching tactics since NATO’s operation began. Many have shed their uniforms and are using weapons mounted on the backs of pickup trucks, just like the rebels, officials said. That led NATO to mistakenly target a column of rebel vehicles this month.

In the meantime, poorly trained rebel fighters are taking a beating as government troops lob long-range rockets into Misurata, with NATO unable to stop them, rebels say.

“They could do better,” said Abdul Bassett Swaisi, the commander of a rebel unit of about 150 men outside Misurata. “If the situation continues to be like this, it will take years, not months.”

The debates raging in the West and allied Arab states have made untenable the prospect of deploying ground troops to push out Gaddafi.

Military analysts say that matters a great deal.

“There’s no example of regime change occurring by bombing alone,” said Shashank Joshi, an analyst at Britain’s Royal United Services Institute, a think tank. In Kosovo, he pointed out, where the NATO air campaign was significantly more forceful than it is in Libya, the threat of deploying ground troops was what finally prompted Slobodan Milosevic to surrender.

Although it is difficult to know whether Tripoli residents are being earnest when they speak to Western journalists in the presence of government minders, recent street interviews suggest there is growing anger in the capital about NATO’s campaign.

Abdul Adeem, 44, an electrician who lives near a house leveled after a NATO strike last week, said the bombing campaign has made people rally around Gaddafi.

“All neighbors are afraid,” he said. “They think maybe NATO will do it again tonight.”

Londono reported from Tripoli. Staff writer Karen DeYoung in Washington and special correspondent Portia Walker in Misurata contributed to this report.