Yet even as they denounce President Assad and call on him to go, Western leaders hesitate. Would the sudden collapse of the Baathist regime open the door to freedom, or would it be the signal for all-out war that sucked in most of Syria's neighbours? And if the rebels came to power, would they be any better than Assad? Or would they impose a new Islamist extremism on the country, turning Syria into a new hotbed of terrorism and anti-Western militancy?
It is no secret that most Western leaders are losing patience with the Syrian Opposition. It is weak, fragmented, quarrelsome and ineffective. Its leaders abroad have little control over the rebels fighting street by street in Homs, Aleppo and Idlib. The various factions spend more time in power struggles against each other than in building a unified campaign against Assad. There are few now who are committed to democratic pluralism, liberal reform or the freedom of speech. Instead, the opposition on the ground appears dominated by shadowy jihadist groups, some with links to al-Qaeda, that have come in from outside to hijack the revolution and turn Syria into an Islamist state. And their fighting tactics are beginning to cause alarm and revulsion. A video clip circulated recently that showed rebels lining up terrified captives, young government soldiers who pleaded for their lives, and shooting them all in cold blood.
For months, Western leaders have been urging the Syrian National Council to heal its rifts, put forward a clear plan for taking power and bring in the leaders of minority groups and those fighting on the ground. But such advice has had little effect. And so last month the exasperated Obama Administration issued a veiled ultimatum: unless the Syrian National Council reformed its structure, it would no longer be regarded in Washington as the visible leader of the opposition. Hillary Clinton, the Secretary of State, poured scorn on SNC leaders who had not set foot in Syria for the past 30 or 40 years, and called for a new meeting in Qatar to replace the SNC with a broader, more representative body.
For some months already, Western leaders have worried about backing an opposition that is more and more dominated by the Muslim Brotherhood, now exiled in Turkey, and seems ready to welcome extremists into its midst. The opposition largely comprised Sunni Muslims and made no effort to attract support from the Kurds, the Christians, the Alawites or any of the many religious and ethnic factions in Syria. As a result, many of these minority groups, especially the Christians, have become deeply suspicious of the rebels' agenda, are alarmed by government warnings that terrorists and extremists are trying to take over Syria. They have been persuaded, for the moment at least, to continue backing the Assad government.
Previous Western attempts to unify and broaden the Syrian opposition have ended in spectacular failure. Last June a meeting of exiled leaders in Cairo broke up amid acrimonious shouting and brawling. But already some leftist opposition leaders are accusing the United States of trying to set up a puppet government in exile and trying to control the opposition agenda.
But as the fighting intensifies in Aleppo and other Syrian cities, with around 1,000 people being killed every week, Western leaders are being urged to supply rebel fighters directly with arms. Unless they do, the opposition has warned, the fighters will increasingly be forced to rely on extremists and other anti-Western jihadists who are now active on the ground. Up till now the West has refused to do so, providing only medical supplies and communications equipment. Saudi Arabia and Qatar, however, make no secret of the weapons supplies they are sending to the rebels from across the Turkish border, and David Cameron, the British Prime Minister, discussed this in a recent visit to the Gulf.
The dilemma for the West is that unless there is massive intervention in Syria, similar in scale and scope to the support given to the anti-Gaddafi fighters in Libya, the forces fighting the Assad regime have little chance of victory, and their campaign is simply prolonging the bloodshed as both sides reduce Syria cities to rubble. But the logistics of intervention are very different from Libya. There is no military aim, no clear geographic divisions between rival sects and ethnic groups, no long-term strategy and no support from Western public opinion for another attack on a Muslim country.
Mr Cameron therefore said during his Gulf visit that Britain would be willing to allow Assad safe passage out of Syria to exile somewhere else if this would help to stop the fighting. And he gave a warning that extremism would grow if the fighting continued. Already the Syrian conflict is having serious repercussions in neighbouring countries. Open clashes have already taken place in Lebanon between Sunni and Shia groups, leading to fears that this could plunge Lebanon back into devastating full-scale civil war. In Jordan, the huge influx of Syrian refugees is worsening social tensions and fuelling the opposition of Islamists to the monarchy. And in Turkey, the Syrian conflict is posing a real challenge for the Islamist government, which has given strong verbal backing to the Opposition but is wary of any military involvement. Opinion polls in Turkey show that around 75 per cent of Turks oppose intervention. But the credibility of Prime Minister Recep Tayyip Erdogan is coming under strain. He is angered that Syria is now openly backing Kurdish PKK rebels in Turkey, but his calls for a no-fly zone and a safe haven for Syrian refugees is impossible without military backing from Turkey's Nato partners. Turkey is also worried that the clashes in Syria risk opening up long-suppressed tensions between the ethnic and religious minorities in Turkey and its Sunni Muslim majority.
All this means that Western leaders see diplomacy as the only way to halt the bloodshed in Syria. United Nations involvement has been blocked by Russia and China, and the West has accused Moscow of giving the Assad regime all the moral and military support it needs. But it is clear that any diplomatic solution would in the end have to involve both Russia and Iran, Assad's two essential supports. The West has already begun quiet diplomacy with the Kremlin, and Moscow may already be putting some pressure on Assad. But as the efforts of Lakhdar Brahimi, the UN peace envoy, have shown, it is becoming impossible to get agreement even for a temporary ceasefire. All those in Syria still think they can win more by fighting than by talking. Assad recently insisted again on Russian television that he had no intention of giving up power or leaving Syria.
The prospect therefore of prolonged and bloody fighting, with thousands more civilians being killed, looks increasingly likely. It is one of the more urgent issues now facing the newly re-elected President Obama. And it is an issue that will determine the shape of the Middle East and the West's role there for years to come.