I believe that if the constitution is signed and ratified in two-thirds of each district it needs to be, then we will have made a huge step forward. I'm not sure peace just "breaks out" like violence breaks out. However, most of the insurgents are nationalists, and if the Shiites can reach an agreement with the nationalist Sunnis (the chances of this are, admittedly, debatable) then most of the gas will be taken out of the insurgency. Most of the suicide bombers, on the other hand, are foreign terrorists. They are certainly in cahoots with the nationalists, but since they're the ones blowing themselves up, they're probably largely viewed as little more than cannon fodder, not leaders. If the need for an insurgency dries up, they will probably turn on the Iraqis, even the nationalists, which will only further marginalize them. Until that happens, the U.S. needs to keep troops in Iraq until the foreign suicide bombers are marginalized to the point that the Iraqi military can handle them on their own.
Even if the divide between Sunnis, Shiites, and Kurds continues to widen, the chances of a full civil war are unlikely as long as the U.S. maintains a military presence. You claim there already is a civil war, but that is largely hyperbole. Most news organizations are reporting a growing isolation of the different communities from each other, with incidents of tit-for-tat killings. A real civil war, however, would be if the militias actually turned on each other in full-scale combat, which anybody who doesn't live in a fantasy world knows hasn't occurred yet.
Your claims that the U.S. is supporting the Shiites in a civil war just reveals a tremendous amount of either delusion or ignorance. If we'd support anyone, it would be the Kurds. The Shiites scare the crap out of us because they're so closely tied to Iran. The U.S. has every reason in the world to ensure Sunnis maintain a level of power that will keep Shiites in check, and prevent Iraq from turning into another Iran.
Despite your rather arbitrary assertion that the Sunnis could "take" the Shiites, this is highly unlikely if the U.S. actually took off and allowed a full scale civil war to occur. Iran has already infiltrated top levels of the Shiite hierarchy, and if civil war broke out then the Sunnis would be faced with Shiite army backed by a neighboring country, while they'd have no one to depend on for a similar alliance. Consequently, they'd seek out such an alliance, probably with Syria, which would elevate the conflict from a national one to a regional one. And sh*t, like snow, tends to grow exponentially when it rolls down hill. Even if it takes 7 years to quell the insurgency, this is still better than allowing a massive regional conflict that could potentially devolve into the third world war.