Is the job done?

On Tuesday, U.S. troops will leave Iraqi cities in accordance with an agreement negotiated under President Bush. Although President Obama has largely endorsed the Bush timeline for reducing the U.S. military presence in Iraq, far less clear is the extent to which he has also adopted his predecessor’s appreciation for the importance of achieving America’s strategic goals there.

For all his administration’s mistakes in Iraq, Bush clearly understood the imperative of victory once U.S. forces were committed. He knew that removing our troops under fire would have been disastrous. Al Qaeda and Iran would have been emboldened. American credibility throughout the Middle East would have been shattered. Iraq would have descended into chaos, further destabilizing a region vital to U.S. interests.

More positively, Bush also understood that fulfilling our commitment to help Iraq establish a stable democracy could dramatically advance long-term U.S. interests. The Arab Middle East -- the region that provided the ideology, funding, leadership and foot soldiers for the 9/11 attacks -- would get a powerful example of a successful, modernizing democracy. And the United States would secure a strategic foothold in one of the Muslim world’s historic centers of political, religious and cultural power.

While Western elites may scoff, many people in the Middle East appreciate the validity of Bush’s central strategic insight. A democratizing Iraq -- aligned with the U.S. and endowed with vast oil reserves, water resources and a large, industrious population -- could transform their region for the better, bolstering the forces of progressive reform at the expense of Sunni and Shiite extremists.

Under Obama, Bush’s commitment to winning in Iraq has all but vanished. Convinced from the start that the war was a mistake (a conviction fortified by the Bush team’s post-invasion bungling), Obama has for years been the salesman in chief for a narrative of failure: Iraq is seen as a colossal disaster -- a senseless distraction that drained U.S. resources while alienating the rest of the world. While recognizing a vague obligation to help Iraqis forge a better future, Obama’s bottom line comes through loud and clear: The war was a strategic blunder, and the sooner the U.S. can wash its hands of it and re-focus on our “real” priorities in the Middle East, the better.

Given that Obama has largely adopted the Bush timetable for withdrawing U.S. forces, one can ask whether it really makes any difference that he still sees Iraq more as a liability to be escaped than an asset to be secured. The short answer is yes. Psychology in international affairs can have strategic effects.

When Bush authorized the U.S. troop “surge” in Iraq, the psychological impact was arguably as important as the military one. Amid insurgent claims of victory and hemorrhaging U.S. domestic support, Bush’s decision to double-down rather than retreat sent friend and foe alike a powerful message that the U.S. had no intention of abandoning Iraq. Reassured, Iraqis were galvanized in their efforts to confront Al Qaeda and Iranian-backed militias, and recommitted themselves to building an independent, pluralist democracy.

Obama risks fueling the reverse dynamic. Iraqis listen to his speeches and hear that withdrawal, not victory, is his highest priority. They see that America appears more concerned with engaging a hegemonic Iran than consolidating a democratic Iraq. On their visits to Washington, they knew that, until the position was finally filled last week, no senior official close to the president had been charged with overseeing Iraq policy.

“Are you Americans still here?” a top Iraqi leader asked me only half jokingly during a recent visit to Iraq. The vacuum being created by the perception of growing U.S. disinterest is palpable. At least before this month’s turmoil in Iran, the void was being filled increasingly by the Islamic Republic. Iranian influence operations had escalated significantly since the Obama administration entered office, manifested most obviously in a surge of high-level Iranian visitors to Iraq.

Once again deeply uncertain about America’s long-term commitment to their future, Iraqis are starting to hedge their bets in unhelpful ways. Accommodating themselves to the agenda of the coming Iranian hegemony rather than their departing American liberators is increasingly the order of the day.

Although the Bush administration made many costly mistakes in Iraq, the surge was a resounding success that put the goal of an independent, democratic Iraq back within reach -- as evidenced by January’s successful provincial elections. Obama is in position to achieve that goal, but only if the U.S. military withdrawal is offset by a corresponding deepening of high-level diplomatic and economic engagement. That, however, will require the president spending far less time signaling his eagerness to get out of Iraq and more time working with Iraqis to figure out how best we can stay.