Are the conditions for success in Iraq really achievable?

Decades ago, the US got involved in war in Vietnam and failed miserably. After the US withdrew, S Vietnam was conquered by the North thereby achieving the very objective the US fought and shed so much blood to prevent.

It is my belief that the US failed in Vietnam because the conditions for victory doomed US efforts from the very start. The US wanted to keep S Vietnam from becoming communist but also didn't want to escalate and expand the war. This, more than war protests at home, proved the undoing. If the US was unwilling to move into N Vietnam or some neighboring countries such as Laos where N Vietname forces were based, to engage N Vietnamese forces, then despite the massive bombing, N Vietnam, with assistance from USSR and China, could threaten and attack S Vietnam indefinitely and continue to inflict casualties on the US forces in Vietnam. But if the US wanted to wipe out the N Vietnamese threat by moving into N Vietnam and/or Laos, China would have entered the war as they did in Korea and the US did not want to start WWIII over Vietnam either. It was supposed to be limited to protecting S Vietnam only. Because of this paradox, the US ulimately failed because the conditions for success made victory impossible.

Now in Iraq, the US might also be caught in a similar paradox. The best case scenario is that there is an uprising, the regime falls and the US is welcomed into Baghdad as liberators. However, if this fails to happen and the regime maintains control and fights dirty and stubbornly and prolongs the war and causes casualty counts to go up, the US might be forced to escalate its attacks and cause more collateral damage. We all know that if the US brought its full might to bear without disregard to collateral damage, the US would be able to defeat the regime. Of course bombing Baghdad to the stone age and killing millions in the process would make operation "Iraqi Freedom" seem somewhat absurd. On the other hand, if the US tries to limit collateral damage and fight a more careful war, it might discover that the resistance is too well dug in and doing so would risk greater US casualties, which is also unacceptable.