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. 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 Islamist 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.” The entity McCain was referring to - Al-Qaeda in Mesopotamia, also known as Al-Qaeda in Iraq - did not exist until after the United States invaded Iraq in 2003. The most recent National Intelligence Estimates consider it the most potent offshoot of Al-Qaeda proper, the group led by Osama Bin Laden that is now believed to be based on the Pakistan-Afghanistan border. It is a largely homegrown and loosely organized group, according to the official American military view that McCain endorses, is led at least in part by foreign operatives and receives fighters, financing and direction from senior Qaeda leaders. In longer discussions on the subject, McCain often goes into greater specificity about the entities jockeying for control in Iraq. Some other analysts do not object to McCain's portraying the insurgency (or multiple insurgencies) in Iraq as that of Al-Qaeda. They say he is using a “perfectly reasonable catchall phrase” that, although it may be out of place in an academic setting, is acceptable on the campaign trail, a place that “does not lend itself to long-winded explanations of what we really are facing,” said Kenneth M. Pollack, research director at the Saban Center for Middle East Policy at the Brookings Institution. But some students of the insurgency say McCain is making a dangerous generalization. “The US has not been fighting Al-Qaeda, it's been fighting Iraqis,” said Juan Cole, professor of history at the University of Michigan and a fierce critic of the war. A member of Al-Qaeda “is technically defined as someone who pledges fealty to Osama Bin Laden and is given a terror operation to carry out. It's kind of like the Mafia,” Cole said. “You make your bones, and you're loyal to a capo. And I don't know if anyone in Iraq quite fits that technical definition.” Al-Qaeda in Mesopotamia is just one group, though a very lethal one, in the stew of competing Sunni insurgents, Shiite militias, criminal gangs and others that make up the insurgency in Iraq. That was vividly illustrated last month when the Iraqi army's unsuccessful effort to wrest control of Basra from the Shiite militia groups that hold sway there led to an explosion of violence. In recent months, McCain has also been talking more about the threat posed by Iranian influence in Iraq, bringing him in line with American military officials, who in the wake of the Basra fighting seem increasingly convinced that Iranian support for Shiite groups now constitutes the primary security threat in Iraq. McCain acknowledged those concerns in an interview with Chris Matthews on MSNBC when he said that “we now see the Iranians beginning to reassert an age-old Persian ambition, as you know, to increase their influence, particularly in southern Iraq.” In talking about both threats, McCain tripped up last month on a visit to the Mideast, when he mistakenly said several times that the Iranians were training Qaeda operatives in Iran and sending them back to Iraq. Prompted by one of his traveling companions, Senator Joseph I. Lieberman of Connecticut, McCain corrected himself, saying that he had misspoken and had meant to say Iran was training “other extremists” in Iraq. And McCain went beyond what he usually says and what his foreign policy advisers believe during a back-and-forth with Obama at the end of February. It began when Obama said at a Democratic debate that while he intended to withdraw American forces from Iraq as rapidly as possible, he reserved the right to send troops back in “if Al-Qaeda is forming a base in Iraq.” McCain seized on the remark. “I have some news,” he said at a town-hall-style meeting in Tyler, Tex. “Al-Qaeda is in Iraq. It's called ‘Al-Qaeda in Iraq.' My friends, if we left, they wouldn't be establishing a base. They'd be taking a country, and I'm not going to allow that to happen.” In general, Obama's views track with those of many independent analysts. In a speech last August, he criticized President Bush by saying: “The president would have us believe that every bomb in Baghdad is part of Al-Qaeda's war against us, not an Iraqi civil war. He elevates Al-Qaeda in Iraq - which didn't exist before our invasion - and overlooks the people who hit us on 9/11, who are training new recruits in Pakistan.” Senator Hillary Clinton, who wants to begin withdrawing troops, has spoken of leaving some troops behind to fight Al-Qaeda, deal with insurgents, deter Iranian aggression, protect the Kurds and possibly help the Iraqi military. She warned last year of the dangers if Iraq turned into a failed state. – The New York Times __