Washington ? President Bush unleashed the U.S. Marines in Fallujah and Don Rumsfeld at the Pentagon within days of securing a second term. A campaign season of playing it safe on Iraq makes way now for a concerted effort to find a new political order and a different military direction in the war there.

The grim task of retaking Fallujah will help determine the viability of Bush’s renewed effort and of the American military presence in Iraq, which cannot remain static. This is where a recently, relatively taciturn Rumsfeld strides back into the picture.

In one sense, a visitor to the defense secretary’s cavernous office can catch a glimpse of the ultimate goal for which the Marines and Army units have been fighting in Fallujah by glancing at a glass-topped conference table.

Beneath the glass lies a sample ballot from Afghanistan’s presidential election. Given to Rumsfeld last month by Hamid Karzai, the election’s winner, the ballot represents for the secretary a telling American political-military success in the war on terrorism — and a future that could soon be in the grasp of Iraqis.

Retaking Fallujah is intended to help clear the way for Iraqi elections in January. But as Rumsfeld pointed out to his theater commanders in a well-publicized memo on metrics a year ago, measuring success in this kind of operation is no easy or sure thing.

The key targets of the renewed offensive in the Sunni heartland are not in fact the headline numbers of insurgents killed or captured, or bomb factories seized or obliterated. As Americans learned to their grief in Vietnam, such physical measurements are elusive and illusory in guerrilla warfare.

Fallujah is part of a battle for minds rather than “hearts and minds.” In the four Sunni provinces that are in bloody revolt against the U.S. occupation force and the interim government of Prime Minister Ayad Allawi, the most important immediate objective is to dissuade Sunni townspeople from joining, supporting or tolerating the insurrection.

The price they will pay for doing so is being illustrated graphically to them in the streets of Fallujah. But what follows this demonstration effect of firepower — that is, what Allawi’s unsteady and unpopular administration can do to convince the Sunnis and others in Iraq that they have a stake in peaceful elections in January — will be the decisive part of this struggle.

That conclusion is reflected not only in the visible importance the Pentagon’s boss attaches to Afghanistan’s ballot but also by the stunningly clear words spoken on Oct. 8 by Lt. Gen. James T. Conway, the Marine commander at last April’s aborted battle for Fallujah. Conway, who is now director of operations for the Joint Chiefs of Staff, said this in a speech at the George P. Shultz Lecture Series in San Francisco:

“I believe there will be elections in Iraq in January and I suspect very shortly afterwards you will start to see a reduction in U.S. forces — not because U.S. planners will seek it, but rather because the Iraqis will demand it.

“I used to think that Americans were impatient,” Conway continued, “but we don’t hold a candle to the Iraqis. We are seen as infidels and nonbelievers, and further, most Iraqis now consider us occupiers. They will expect us to provide regional security for a long time because we have destroyed their army. But they will be willing to accept risk as regards internal security, in exchange for a reduced coalition presence. I think our strategic planners have got it right.”

Doing more with less is the overwhelming lesson of Afghanistan, Rumsfeld constantly reminds aides. The performance of the several thousand newly trained Iraqi soldiers who accompanied the division-sized Marine force into Fallujah is the other essential part of the demonstration effect there, as Rumsfeld hinted in a Pentagon news conference on Monday.

It was his first briefing for Defense Department reporters since Sept. 7. Asked about his absence from the podium, Rumsfeld said Bush had asked him and Secretary of State Colin Powell to keep low profiles during the campaign.

That enabled the White House to practice tighter damage control on foreign and defense policy. But such caution also granted the insurgents time to prepare. The costs this may have involved will only now become clear as the key battles for the Sunni heartland begin in earnest.

— Jim Hoagland is a columnist for Washington Post Writers Group.