......... -- not combat troops, but military advisers, special operations forces, to watch the counterterrorism effort." This Statement is rated Mostly True according to the Politifact truth-o-meter.
For a period, at least, the Obama administration did envision leaving 10,000 troops in Iraq past the Dec. 31, 2011, pullout of forces. That number went down to about 5,000 before negotiations stalled amid a legal snare over immunity of American forces in Iraqi courts.
Some History......
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.
Military commanders in Washington and in Baghdad pushed for a residual force between 16,000 and 24,000 to conduct counterrorism work and train Iraqi security forces.
The White House, reports show, was not open to a force that size.
The Obama administration was initially open to leaving up to 10,000 troops in Iraq after the scheduled pullout at the end of 2011, a controversial pitch that would have required approval from Iraq’s divided government to change the 2008 agreement, the Los Angeles Times reported. The troops were to be placed in Baghdad and other "strategic" locations around the country.
It did not stay there. The New York Times detailed how the one-time goal of a 10,000-person force shrank before negotiations failed altogether.
Obama ruled out the 10,000-troop option in an Aug. 13, 2011, conference call, according to the New York Times, and "the new goal would be a continuous presence of about 3,500 troops, a rotating force of up to 1,500 and half a dozen F-16’s."
What killed the deal? The agreement failed over a demand that American troops be given immunity from prosecution by Iraqis, a very touchy political issue within the Iraqi Parliament. Some experts said Iraqi leaders may not have been willing to take great political risk with their citizens in exchange for a relatively small American force.
But no immunity meant no sizable residual troop presence. "When the Americans asked for immunity, the Iraqi side answered that it was not possible," al-Maliki said in an October 2011 news conference. "The discussions over the number of trainers and the place of training stopped. Now that the issue of immunity was decided and that no immunity to be given, the withdrawal has started."