(CNN) -- "Gadhafi must go. And go for good."
That was the ringing declaration in an op-ed piece from U.S. President Barack Obama, French President Nicolas Sarkozy and British Prime Minister David Cameron, published Friday. The same conclusion was reached at the Qatar meeting of the Libyan contact group this week.
The Libyan leader's removal may not be part of the mandate agreed on by U.N. Security Council resolutions, but it is very much part of the international mission.
The unanswerable question remains: How?
The British and French governments have complained that they are shouldering too much of NATO's aerial mission now that the United States has receded into a support role. Friday, the Italian government only compounded that frustration by declining to carry out airstrikes.
"The whole government is agreed that Italy's present line is correct and we will not modify our support for the military operation in Libya," said Defense Minister Ignazio La Russa. The Italians currently help enforce the no-fly zone.
Pro-Gadhafi forces are still laying siege to Misrata, where civilians are dying every day from rocket and artillery strikes. Vague hopes that the regime would somehow implode have come to naught despite more than 900 strike sorties since April 1.
There is no consensus on arming the rebels.
Italy says it's open to the idea. In Qatar this week, Foreign Minister Franco Frattini said, "Either we make it possible for these people to defend themselves, or we withdraw from our obligation to support defending the population of Libya."
Qatar says it is in the process of supplying the opposition with anti-tank weapons.
France and the United Kingdom say not for now. "France is not currently in that frame of mind," was the curt response from French Foreign Minister Alain Juppe on Thursday when asking about arming the opposition.
There is also much hand-wringing over the rebels' lack of organization and training. Two weeks ago, U.S. Defense Secretary Robert Gates said of the rebels: "It's pretty much a pick-up ballgame, with no command and control." One NATO diplomat Friday scoffed at the idea the rebels would be able to mount a serious military threat against the regime, describing it as a fantasy.
And while Gadhafi's forces have been seriously degraded by almost a month of airstrikes, NATO officials acknowledge they have adapted and are now much more difficult to hit, hidden in urban areas and often using pickup trucks rather than military transports.
Some observers are reminded of the NATO air campaign against Yugoslavia in 1999, when it took 78 days of bombing against an already weakened adversary to persuade Slobodan Milosevic to sue for peace. As a recent study by the Rand Corporation concludes: "What began as a hopeful gambit for producing Milosevic's quick compliance soon devolved, for a time at least, into a seemingly ineffectual bombing experiment with no clear end in sight."
In the midst of all these difficulties, now is the time to hang tough, says U.S. Secretary of State Hillary Clinton. Acknowledging "Gadhafi is testing our determination," she said Thursday that NATO needs to maintain its resolve and unity.
Writing in the Washington Post Friday, NATO Secretary General Anders Fogh Rasmussen agrees there is a vigorous debate over NATO's mission. He is confident it will succeed. "Our actions mean that the pro-Gadhafi forces cannot fight where they want, cannot fight how they want and cannot use the weapons that they want against the civilian population," he writes.
But Rasmussen also agrees with the viewpoint most often expressed by Germany, France and Turkey, that Libya's civil war cannot be resolved by force alone. "That is why the international community is urgently seeking a political settlement. A settlement that ensures that the people's legitimate demands for genuine transition," he writes.
Transition has become the buzzword. Earlier this week, Clinton said there needs to be a "transition that reflects the will of the Libyan people and the departure of Gaddafi from power and from Libya."
Those last three words are non-negotiable to Libya's inner circle, according to sources in Tripoli that have spoken to CNN in recent weeks. They say Moammar Gadhafi is ready to relinquish power once peace is restored, but exile is out of the question.
His son Saif, an influential figure in the Libyan leadership, told a French TV network this week: "The Libyan Guide (his father) does not want to control everything. He is at an advanced age. We would like to bring a new elite of young people onto the scene."
"We need new blood -- that is what we want for the future -- but talk of the Guide leaving is truly ridiculous," he was quoted as saying.
So a rock meets a hard place, made harder still by this line in the Obama/Sarkozy/Cameron piece: "The International Criminal Court (ICC) is rightly investigating the crimes committed against civilians and the grievous violations of international law." The message: not only must Gadhafi leave Libya; he should expect to be pursued for war crimes.
The chief prosecutor of the ICC, Luis Moreno Ocampo, told CNN last month: "I am 100% sure that there will be enough evidence to present a strong case on the investigation very soon. We have to be confident that we have a strong case. The issue now is how to link this with authorities."
"That's not much of an incentive for Gadhafi to do a deal," said one European diplomat. "He might as well stay and fight."
Other officials are critical of the way the first U.N. Security Council resolution (1970) was drafted to include the possibility of action against Gadhafi by the ICC, and by the public insistence of many governments that he must go into exile. They say it left no room for negotiating a political solution amid a stalemate on the battlefield.
Several parties talk of a road map to a political solution, most notably Turkey -- the only country represented in both the rebels' headquarters, Benghazi, and the capital, Tripoli, and one long influential in Libya. Prime Minister Recep Tayyip Erdogan said last week it "envisages a peaceful transition process and protects the territorial integrity and sovereignty of Libya."
But speaking to CNN Friday, the Turkish ambassador in the United States, Namik Tan, said there would be no short cuts and no magic formula in Libya, even if there were international agreement that Gadhafi must step down.
The African Union found out the hard way -- its delegation to Libya struck a deal with Gadhafi before being firmly rebuffed by the opposition because the terms did not include Gadhafi's immediate departure
At the same time, the United States -- and other governments -- are wary of too close an association with the opposition.
The rebels have requested access to some of the billions in frozen Libyan assets, but some diplomats say that would be tantamount to recognizing them as the legitimate representative of the Libyan people. The United States in particular is haunted by experiences in Iraq and Afghanistan, where backing opposition groups with arms and money backfired, and is wary at the possibility of growing Islamist influence within Libyan rebel ranks.
Four weeks after the coalition began bombing regime targets in Libya, the ultimate destination of any road map still seems at best uncertain.