As he campaigns with the weight of a deeply unpopular war on his shoulders, Senator John McCain of Arizona frequently uses the shorthand “Al Qaeda” to describe the enemy in Iraq in pressing to stay the course in the war there.

“Al Qaeda is on the run, but they’re not defeated” is his standard line on how things are going in Iraq. When chiding the Democrats for wanting to withdraw troops, he has been known to warn that “Al Qaeda will then have won.” In an attack this winter on Senator Barack Obama of Illinois, the Democratic front-runner, Mr. McCain went further, warning that if American forces withdrew, Al Qaeda would be “taking a country.”

Critics say that in framing the war that way at rallies or in sound bites, Mr. McCain, the presumptive Republican nominee, is oversimplifying the hydra-headed nature of the insurgency in Iraq in a way that exploits the emotions that have been aroused by the name “Al Qaeda” since the Sept. 11 attacks.

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There has been heated debate since the start of the war about the nature of the threat in Iraq. The Bush administration has long portrayed the fight as part of a broader battle against Islamic terrorists. Opponents of the war accuse the administration of deliberately blurring the distinction between the Sept. 11 attackers and anti-American forces in Iraq.

“The fundamental problem we face in Iraq is that there is not a single center of gravity, as in the cold war, but a whole constellation of contending forces,” said Bruce Hoffman, a terrorism and counterinsurgency expert at Georgetown University. “This is much more fractionated than most people could imagine, with multiple, independent moving parts, and when you have that universe of networks, you can’t have a one-size-fits-all approach.”

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