As US cruise missiles destroyed Libyan air defence batteries and French fighters took out four tanks attacking the rebel stronghold of Benghazi, Mr Obama told the world that he had no choice but to launch "limited" military action to prevent Colonel Muammar Qaddafi realising his brutal intentions. But Mr Obama's key message was aimed at Americans: "We will not - I repeat - we will not deploy any US troops on the ground." The New York Times reports that Mr Obama had also insisted to his aides that US military involvement must be over within "days, not weeks".
Western leaders have made no secret that they want Col Qaddafi out, with Mr Obama, Mr Sarkozy and the British prime minister David Cameron all having declared unambiguously that the Libyan strongman had lost his legitimacy. But their military campaign was adopted as an emergency response to the intolerable probability that without foreign intervention, Col Qaddafi could sack the rebel capital of Benghazi and exact vicious reprisals on an epic scale.
Optimists in western corridors of power hope that the "shock and awe" effect of their air campaign prompts the regime's collapse amid mass defections. But optimism is the opiate of the interventionists, and western leaders would do well to prepare for some nastier contingencies. It's almost inevitable that mistakes by coalition pilots result in civilian casualties - a scenario Col Qaddafi will work hard to engineer by the placement of his military resources, and whose probability was underscored on Saturday when rebel fighters in Benghazi appeared to have downed a fighter jet piloted by one of their own.
More importantly, even when in an aggressive fashion, air power rarely succeeds on its own in dislodging an enemy. UNSC Resolution 1973 allows the use of force only to protect civilians, however, and not to provide air support to a rebel military advance. The Security Council has also forbidden governments from arming the rebel forces, as Egypt's military is reported to be doing already, albeit discreetly.
The resolution, instead, ties the protection of civilians to the demand for a cease-fire (by all sides) and a negotiated political solution. That gives Col Gaddafi's regime considerable wiggle room. Although Tripoli initially announced its acceptance of the ceasefire, it never stopped its advances on rebel strongholds. Still, a truce remains an option at any time, as Mr Sarkozy himself conceded, "opening the door" to resumed diplomacy that could become increasingly messy.
Col Qaddafi continues to command a degree of popular support, and is relying on the passion of his supporters, infused by the foreign intervention with national fervour, to even up the odds by starting to hand out weapons, hoping to fight the battle on terms that negate the effectiveness of a western intervention confined to bombing heavy weaponry from the air.
But no one wanted to talk about end games - either a strategy for removing Col Qaddafi, or what would follow his ouster - last week as the tyrant's forces bore down on Benghazi. This war was forced by an urgent need to do something to stop Col Qaddafi crushing the rebellion and butchering tens of thousands of civilians. The "realist" camp in the Obama Administration, led by the defence secretary Robert Gates and the national security adviser Tom Donilon, were focused on strategy, consequence, and end-game, and on that basis warning Mr Obama against getting involved in a conflict whose outcome was not vital to US national interests. But Col Qaddafi's blitzkrieg tipped the scale in favour of humanitarian military intervention, as advocated by the US secretary of State Hillary Clinton, her top adviser Samantha Power, and Susan Rice, the US ambassador to the UN.
Despite Mr Obama's statements on limits of the engagement, the realists know that wishful thinking will count for little. The urgency of responding to Col Qaddafi's march on Benghazi with murderous intent had prompted Western leaders to set aside questions of an endgame in launching military action.
Interventions that are not guided by a strategy, but by good intentions, don't always lead to happy outcomes. The enemy usually has some ideas of his own about how the war will be fought.