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“From a straight propaganda and recruiting standpoint, if we lose there, if we show them we are what bin Laden called the ‘weak horse,’ then their recruiting is going to go through the roof,” he said. “If they can show they are successful there, that is an incredible propaganda boon.

“Also, al Qaeda’s donors and supporters love a winner. If al Qaeda can show them they can win there, their coffers will fill up from their big donors,” Mr. Roggio said.

Douglas Feith, who as the Pentagon’s top policy official at the time of the Sept. 11 attacks was an architect of the war on terror, said leaving Kabul would hurt the counterterrorism campaign worldwide.

“There are many serious bad consequences of losing the war,” Mr. Feith said. “The Taliban will gain in Afghanistan and may help terrorists against us again. The Taliban would gain Pakistan and may destabilize the government there, which has nuclear weapons.

“Jihadists worldwide and other U.S. enemies would be emboldened by our defeat,” he said. “Afghans who cooperated with us would suffer. Others in the world would be reluctant to cooperate with us in the future.”

Mr. Panetta said the war’s mission is to prevent more attacks.

“Our purpose, our whole mission there is to make sure that al Qaeda never finds another safe haven from which to attack this country,” he told ABC News. “That’s the fundamental goal of why the United States is there.”

Fewer Americans are buying that argument. A recent CNN/Opinion Research Corp. survey found that 41 percent of Americans support the war, down 9 percentage points from May 2009.

In August 2009, as President Obama was sending reinforcements to Afghanistan and Gen. McChrystal was asking for even more troops, a Washington Post poll detected growing disenchantment. Fifty-one percent said the war was no longer worth fighting, up 6 percentage points from previous month. Two months ago, the number grew to 53 percent.

A new NBC poll found that 70 percent of Americans do not think the U.S. will win in Afghanistan.

Three factors seem to drive the numbers: the war’s length, now in its 10th year; the number of casualties, including the 125 Americans killed in June and July; and the cost of war-related spending for Afghanistan, which the Congressional Budget Office says will reach $300 billion this year.

The House this year delayed for months a vote on a war-funding bill as a growing number of Democrats voiced opposition. When a vote was taken on July 28, 102 Democrats, more than double the number of a year ago, voted no.

The number of congressional Democrats abandoning Mr. Obama on the war has not yet translated into a groundswell of opposition nationwide.

Still, grass-roots anti-war groups are active. One is Veterans for Peace, a 7,500-member group based in St. Louis that also criticizes Israel and is supporting Army Pfc. Bradley Manning, the intelligence analyst suspected of providing thousands of pages of classified State Department and military reports on Afghanistan to

“VFP is opposed to the war in Afghanistan for several reasons, but the primary one is that it is an illegal war of aggression which has killed thousands of innocent people,” said Leah Boyer, the group’s vice president and a retired Navy commander who is now is now a full-time peace activist.

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