Some have argued that the White House never fully engaged to keep U.S. troops in the country and that the presence of a small contingent now could have kept the peace. Others say Maliki would never have agreed to allow the Americans to remain and their presence to defend his government wouldn't have made much difference since, as Marc Lynch puts it, he's the main problem in the first place.
Like it or not, American political realities come into play here. Barack Obama first rose to prominence as the most prominent Democratic candidate who opposed the war in Iraq. Given that he was elected in large part to end the war, and that the war continued for three years and hundreds more soldiers died under this presidency, it's not very realistic to expect that he would have expended much effort and capital prolonging a military operation that neither the Iraqi government nor the American people supported anymore.
I'm inclined to agree with Douglas Ollivant that if you're going to blame Obama for something, it's his administration's handling of Syria rather than its disengagement from Iraq.
In 2011, when the uprising in Syria began and it became clear that Bashar al-Assad wasn't going to fold as easily as his counterparts in Egypt and Tunisia, America was faced with two bad options and picked neither.
The U.S. could have given strong support to the Syrian rebels back when the actually were Syrian rather than international jihadist interlopers like ISIS, as advocated by former Amb. Robert Ford and, reportedly, much of Hillary Clinton's State Department. This support would have to be enough to actually tip the balance of the conflict against Assad's Iranian and Russian-supported forces.
Or, the White House could have just stayed out of it, pressing for international sanctions and providing as much humanitarian assistance as possible to refugees fleeing the conflict while doing nothing directly to stop Assad's forces from crushing the opposition.
Neither option would have turned out well. If he pursued the latter, Obama would be accused - justifiably - of turning a blind eye to a massacre. (It's also possible Turkey and the Gulf States would have stepped in to support the rebels anyway.)
If he pursued the former, Obama would be accused - justifiably - of responsibility for the inevitable chaos that would follow the collapse of the Assad regime. (See: Libya.)
These are both grim options and likely neither would have been popular and both would have led to other unpredictable outcomes, but at this point it seems likely that both would have resulted in fewer Syrian casualties and less regional chaos than the middle path that the administration did choose: supporting the rebels enough to keep them fighting, but not enough and with so many conditions as to not actually allow them to win.
At one point, there was a case to be made that this made a kind of amoral grand strategic sense: It kept Iran, Hezbollah, al Qaida, and even Russia pouring resources into a conflict that the U.S. was only minimally involved in. But after more than 160,000 deaths in Syria, the spread of Syria-related violence first to Lebanon and now - in far more dramatic fashion - to Iraq, and the rise in eastern Syria of the most dangerous and effective extremist group the Middle East has seen in quite some time, it's fair to say that the middle path hasn't worked out very well.
As the administration contemplates another choice between two bad options -- intervening with drones or arms to protect Maliki's government or just leaving Iraq to its fate - that's probably something to keep in mind.
- Slate