I've not had time to read all the comments carefully, but this thought crosses my mind after skimming what various commenters have said:
The right views victory in Iraq as important for presenting a strong face to the enemy. Hence, the right is averse to withdrawal, which smells like appeasement. Time and again, history has shown that appeasing an enemy serves merely to embolden that enemy. Case in point, of course--dealing with Hitler in the 1930's.
Also, some on the right feel that a stable Iraq will lead to stability in the Middle East. Additionally, some of the right feel that regime change in Iraq can serve as a model for other Middle Eastern countries.
The left, on the other hand, sees the American presence in Iraq as the problem in the Middle East. Were the United States to withdraw, the Middle East would settle down. What historical examples can the left offer to substantiate their position? Or is the situation so unique as not to offer examples?
In sum, the right believes that the costs of staying far outweigh the costs of withdrawal. The left, of course, believes the opposite.
Perhaps the above is simplistic and a misinterpretation of the discussion which has been going on here in my absence. Feel free to correct me.
[Hat-tip to The City Troll for giving me the idea of transferring one of my comments]