Sunday show pundits weighed provocations by the Islamic State this week after the public beheading of American journalist James Foley, with some military analysts arguing for a stronger military response from President Barack Obama.

On ABC This Week, retired Marine Gen. John Allen said ending the threat from the Islamic State will require a coalition approach that targets the extreme militant groups across the larger region of Iraq and Syria.

Martha Raddatz, ABC’s chief global affairs correspondent, was wearing her TV pundit hat when she said Allen’s idea for a strategy "makes me think back about what the Obama administration originally wanted."

"They wanted 10,000 troops to remain in Iraq -- not combat troops, but military advisers, special operations forces, to watch the counterterrorism effort," she said. "So perhaps they'd go that way, but it would be a tough one."

The number sounded interesting to PunditFact given Obama’s 2008 campaign pledge to pull out of Iraq entirely (which PolitiFact monitors here ) and his repeated 2012 campaign proclamations that the war was over.

So we decided to check it out.

The plan

Shortly before Obama took office in January 2009, his predecessor, George W. Bush, finalized an important agreement after about a year of negotiations with Iraqi Prime Minister Nouri al-Maliki.

Called the Status of Forces Agreement , it spelled out the withdrawal of all American troops by the end of 2011.

Obama, who won office in 2008 partly for his pledge to end the war in Iraq, announced his own draw-down plans a month after taking office. "Let me say this as plainly as I can: by Aug. 31, 2010, our combat mission in Iraq will end," he said Feb. 27, 2009.

His speech revealed more details: He would keep between 35,000 to 50,000 military personnel there through the end of 2011 to train and advise Iraqi military and for counterterrorism purposes.

What would happen after Jan. 1, 2012, -- a central point in our fact-check -- was not settled until the fall of 2011. Obama and the Iraqi government had been open to leaving more troops behind to help the country remain stable.

But it didn’t happen.

The result

On Oct. 21, 2011, Obama announced the pullout of the vast majority of American troops in Iraq by Christmas. Staying behind were a couple hundred Marines to train the Iraqi army and provide security for diplomatic personnel.

Essentially, he implemented the phase-out plan laid out by Bush.

Facing a re-election challenge, Obama held the drawdown of all troops as the fulfillment of a campaign pledge. He did not harp on what some, namely Republican presidential candidate Mitt Romney, would see as a failure: failure to reach an agreement regarding how many American troops would remain in the country beyond Jan. 1, 2012.

This was something Obama and his defense advisers had pushed for as they wrangled in negotiations with the al-Maliki-led government in the summer of 2011. The administration feared a virtually complete pullout would allow for big attacks from militant groups.

Here’s what they wanted, and why it failed.