The war in Iraq doesn't parallel Vietnam a whole lot. You could stretch things and make it seem like there are similarities, but that's all they are - stretches. With Vietnam, the US was focused in defending South Vietnam from the North Vietnamese and refused to invade North Vietnam - only bomb them. Hence the US wasn't trying to "defeat" the enemy, but rather, wear them out to the point where they stop fighting.
Whereas with Iraq, the US has already gone in, totally defeated the opposing Iraqi army, and even executed the Iraqi leader. Now the US is focused with trying to occupy the country and rebuild it, which was never the case with Vietnam.
Of course, let's not forget that the guerilla fighting in Vietnam was much more severe because the dense jungles and cities in Vietnam make that kind of fighting much easier. You have that kind of fighting in Iraq, but as most of the country is a large open desert or flood plains, you don't have it so much.
I'd say the war in Iraq has far more parallels to the US occupation of the Philippines in 1898 to 1913, where the US had just destroyed the Spanish and took their colony of the Philippines. At the same time, the Philippines were fighting for their independence from the Spanish and believed the US was helping them, only to be stabbed in the back and have a new colonial master - the US. The US justified itself and its casualties in the Filipino resistance on the grounds that it's developing and westernizing the Philippines, which is very similar to today's US's justifications for Iraq (except without the element of terrorism, which has been emphasized ever since Iraq was proven to have not had any WMDs - thus even these two situations paralleling each other is a stretch).