I'm not sure the analogy with Algeria is quite on point. It's certainly true that extreme French coercion lost the battle for hearts and minds, though--notwithstanding Abu Ghraib and other excesses--I don't think U.S. misbehavior in Iraq has been as systemic or widespread as the French's Algeria.

And the disgust of the French people and many in the French military itself for French counterinsurgency tactics combined with de Gaulle's practical realization that France could not maintain colonial control of a country that was increasingly non-French to move France finally to stand down. But the French withdrawal was prefaced by arduous negotiations, and was sufficiently deliberate to leave an intact country which continued, for better or worse, to have close relations with its former colonial master. A variety factors precluded such a result in Vietnam. They included the American electorate's anger over the incompetence and duplicity of its government in prosecuting the war, a high number of American dead relative to the low likelihood of success, a weakly committed and uncooperative host regime, and an absence of U.S. strategic interests strong enough to convince the American people to "stay the course." One of the main points we are trying to make is that all of those factors except for the last obtain with respect to Iraq, and Iraq's strategic importance does not argue for its continued occupation by the United States on account of the perversely antagonistic effect that the U.S. military presence has on Iraqi nationalists, Sunni enemies, and foreign and Iraqi jihadists. The upshot is that the U.S. public's tolerance for the war will keep wearing thin, and eventually force a stark withdrawal. This will leave Washington with fewer rather than more options for controlling the damage--unless we start designing and implementing a more nuanced withdrawal now.