WASHINGTON – President Bush’s choice to head the Pentagon will inherit an unpopular war in Iraq, a straining military mobilized in hot spots around the world and a budget that commanders complain has underfunded their combat needs.

Robert Gates’ biggest hurdle will doubtless be meeting the high expectations for an Iraq exit strategy under pressure from next year’s Democratic-controlled Congress and a war-weary American public.

Given Bush’s suggestion this week that his new Cabinet member, whose Senate confirmation is all but assured, would be a force for change, Gates will be expected to do what the outgoing secretary, Donald Rumsfeld, could not: Figure out how to bring home substantial numbers of troops from Iraq in short order, without surrendering the country to a new insurgency or triggering all-out civil war.

“If anybody had a silver bullet answer for this, the president and the previous secretary would have done it, they would have loved to get the troops out early,” said retired Marine Lt. Gen. Michael DeLong, former deputy commander of the U.S. Central Command during the Afghanistan and Iraq wars.

As a member of the Iraq Study Group, a bipartisan panel that has been asked to help chart a new course in the war, Gates has been immersed in the issue for months. That group is expected to issue its recommendations as early as next month, and they are eagerly awaited by Bush and members of Congress.

Some military leaders have quietly suggested there are ways to reduce the number of U.S. troops in Iraq by restructuring the way coalition forces are being used.

A smaller U.S. presence, they have argued, could lessen tensions and reduce the violence and still provide needed training to the Iraqis. Gates will also have to decide whether to reduce the combat role of American forces there.