To many Iraqis, the United States’ influence is greatly diminished. “American policy is very weak,” observed Fuad Hussein, the chief of staff to Massoud Barzani, the president of the semiautonomous Kurdish region in northern Iraq. “It is not clear to us how they have defined their interests in Iraq,” Mr. Hussein said. “They are picking events and reacting on the basis of events. That is the policy.”

Campaign vs. Reality

As a presidential candidate in 2008, Mr. Obama had one basic position on Iraq — he was going to bring a “responsible end” to the conflict. He vowed to remove all American combat brigades within 16 months, a deadline that enabled him to outflank his main rival in the Democratic primary, Hillary Rodham Clinton, but which the military said was too risky. Once in office, he adjusted the withdrawal schedule, keeping American brigades in place longer but making their primary mission to advise Iraqi forces.

All American forces were to leave Iraq by the end of 2011, the departure date set in an agreement signed by President George W. Bush and Mr. Maliki in 2008. Even so, Mr. Obama left the door open to keeping troops in Iraq to train Iraqi forces if an agreement could be negotiated.

The situation the Obama administration inherited was complex. Many Iraqi politicians were worried that Mr. Maliki, a Shiite, was amassing too much power and overstepping the Iraqi constitution by bypassing the formal military chain of command and seeding intelligence agencies with loyalists. Those concerns were aggravated by the political gridlock that plagued Baghdad after the March 2010 elections.

Convening a videoconference on Oct. 6, 2010, Mr. Biden and top American officials reviewed the options. The vice president favored a plan that would keep Mr. Maliki as prime minister, but which involved installing his main rival, Mr. Allawi, leader of the Iraqiya bloc, near the top of the pyramid. To make way for Mr. Allawi, Mr. Biden suggested that Mr. Talabani, an ethnic Kurd, be shifted from the presidency and given another position. “Let’s make him foreign minister,” Mr. Biden said, according to the notes of the meeting.

“Thanks a lot, Joe,” Mrs. Clinton said, noting that Mr. Biden had cast the Foreign Ministry as a consolation prize.