The military campaign in Libya began with what seemed a narrowly defined mission: To enforce a no-fly zone and protect civilians from attacks.

Two months later, the campaign has evolved into a ferocious pounding of the country’s capital, Tripoli, in what appears an all-out effort to oust Muammar Gaddafi. But that goal remains elusive, raising the prospect of a quagmire in the desert. And the political will of the countries involved is being sorely tested.

The Libyan opposition remains weak. Nato, the North Atlantic military alliance which took over command of the campaign from the US on 31 March, appears to have no clear exit strategy. Two of the allies, Britain and France, have descended into public squabbling over bringing the fight closer to Gaddafi with attack helicopters. And the French foreign minister said his country’s willingness to continue the campaign was not endless.

Part of the challenge lies in the original UN resolution: It authorised the use of air power but forbade ground troops, even as it authorised “all necessary means” to protect civilians following Gaddafi’s brutal suppression of the popular uprising against his rule.

From Yugoslavia to Iraq, recent history has shown that ousting a regime through air power alone is, at best, exceedingly difficult.

In Libya, it is not for lack of trying. What seemed at first to be limited strikes on military targets – tanks heading for the city of Benghazi here, some anti-aircraft batteries there – has now expanded.

The targets have come to include, for example, Gaddafi’s presidential compound; one of the leader’s sons was killed on 30 April. Nato’s official line is that the compound was a command-and-control centre and it was not trying to kill Gaddafi. But clearly no one in the alliance would have shed a tear had the Libyan leader died.

There are signs of frustration, or perhaps desperation, among the allies. To avoid anti-aircraft fire, the campaign at first relied largely on high-altitude precision bombing. But France said that it now plans to deploy helicopter gunships to hit targets more precisely in urban areas while risking the lives of fewer civilians.

So far, no allied servicemen or women have been killed in the campaign. But by using helicopters and flying far lower, the French would be putting their pilots at greater risk, underscoring their intense desire to finish the Libyan operation sooner rather than later.

The danger to pilots could be significant. Although Libya’s surface-to-air missile network has been effectively destroyed, Gaddafi’s forces are said to retain hundreds of heavy machine guns, automatic cannon and shoulder-launched missiles that would pose a danger to helicopters at lower altitudes.

In past conflicts, Nato has shied away from using slow-moving and low-flying helicopters and AC-130 gunships against opponents with such weaponry.

During the bombing of Kosovo and Serbia in 1999, the alliance quickly abandoned plans to deploy Apache attack helicopters after the defenders shot down or damaged half a dozen strike jets in the opening days of the campaign.