History is loaded with promises of quick wars and minimal bloodshed. While it is true that our troops are performing splendidly (as expected), US casualties have been -- thankfully -- almost unbelievably low, and that we may soon see a new government installed in Iraq (perhaps within a week), I would caution against predictions of a quick end to things.
I think we will see a long-term (i.e., permanent) US presence as "peacekeepers", which will make them targets for car bombs, suicide bombers, snipers, and any other sort of dirty tricks those ragheads can dream of. It will be like installing a lightning rod for terrorism.
There have been dicussions bandied about as to how long the US has to maintain a presence to see something like democracy installed. I think the most coherent answer to date has been, "As long as it takes."
My personal misgivings about the US role in all this stem from precisely that: I fear another expensive (both in terms of lives lost and money) expenditure of US resources with no end in sight.
It is nowhere near over.
Given that neither of us knows, just let me say that I rather doubt that this will be the case. Terrorism such as you say you expect generally has to be supported by a populace friendly to that terrorism and willing to shelter and encourage it. But so much of Iraq's population has seen Saddam's dictatorship's brutality for so many years, that I don't think there will be general, lingering illwill toward the U.S. and the Brits. I believe that, as soon as the population is sure Saddam is indeed either dead or, at very least, permanently imprisoned (and dead would be better), then we will see considerable support for the U.S. and Brits. That sort of outcome will not support terrorism against us except for possibly a very few, isolated occurances.
My guess is that many, many more Iraqis will be far more inclined to search out and kill ex-Saddam henchmen and prison personnel than will want to harm us.