Rumsfeld may have sincerely believed that the USA could rush in, take out Hussein, and then leave immediately. We certainly could have done that. The question is, would that have been an even worse situation than OTL?
And the major reason to consider that it might not be, is the supremely counterproductive way Bush mandated the early occupation--and the later occupation--and the whole Iraq mess from beginning to end on his watch--should be bungled.
Just because Rumsfeld may have sincerely believed something doesn't make it right and true. From the point of view of professed goals--to bring democracy to Iraq, to check the rise of anti-American and general anti-Western terrorism, to stop an alleged thread of WMDs, and to eliminate Hussein himself--they achieved only the latter, and belatedly. There never was a serious WMD threat in the first place in Iraq (not saying Hussein might not have posed one if left completely alone, but he wasn't left alone and the isolation and interference he was under left him no effective capacity to develop one) whereas it continues to grow apace elsewhere. Nothing dealt the USA so severe a blow to our prestige globally as the way we handled Iraq. Nothing could have been more provocative than the actual approach we took.
Compared to that clusterfrack, I suppose Rumsfeld's quick-in-and-out notion might hardly have been worse. But only in that light; as a policy it was criminally irresponsible. Even if we had, in the course of a massive bombardment and military curbstomp, also by sheer good luck managed to kill Hussein himself and all his personal offspring, that kind of smash-grab-run would surely have left a somewhat wrecked Iraq seething and liable to fall right back in line behind someone indistinguishable from Hussein. If it were true that there were pro-USA Iraqis waiting patiently for some thunderbolt to take out Hussein, we'd surely have needed to stay to ensure their chances at being the ones to take over. In fact, it is part of the moral and legal (by international law) obligation of a conqueror to hang around to ensure order.
What we did was the worst case; we did hang around, leaving our soldiers in a buzzsaw, but without any planning, preparation, or means available to properly implement our minimal duties as occupying powers, thanks to Rummie's vetos on said planning and in fact the force levels necessary to carry out a reasonable occupation plan. That left not only the Iraqis themselves in the lurch but our own soldiers, as failure to deploy adequate troops to secure what we dislodged the prior regime from meant that massive stocks of weapons of various kinds fell easily into the hands both of disgruntled former supporters of Hussein and his numerous underground opponents.
Now, if we'd done it by the book--the book that American generals who were fired by Rumsfeld were trying to follow, our own doctrines on how to handle an occupation that our own experience has led us to compile--I still think it would have been a mess. We'd have had to initially deploy something like twice as many people and plan to stay for years. To be sure, we might, if all this were intelligently managed, perhaps have made more friends than enemies in Iraq and managed to leave some years before say 2008. But I wouldn't bet much on the Bush Administration being able to approach intelligent management; what they did initially was dead opposite the right approach--well, what the actual invading military forces tried to do, with inadequate resources to be sure, was not entirely wrongheaded, but they were countermanded in short order by Bush's appointed proconsuls.
The big mistake, in my view, was invading at all. I don't think it was ever strictly necessary, and certainly shouldn't have been allowed to happen on Bush's watch.
A bigger mistake was supporting guys like Hussein on their rise to power in the first place; that goes back a long way, to the early 80s in his personal case and to the early '60s in the history of US support for thuggish military coups in Iraq in general. The thing about guys like Don Rumsfeld, Dick Cheney, Colin Powell, and their brain trust in general rolling their eyes at me about spilt milk and waters under the bridge is, these people were the ones who, in the 1980s, spilt that milk under the bridge personally; they were the ones who aided Hussein's rise to the top in Iraq and supported him in his war on the Iranians, with everything from satellite intelligence to helping him develop and deploy the same chemical WMDs that we later used to rhetorically hang him.
So who knows what Donald Rumsfeld thinks in his doublethinkful, Bigbrotherful little mind. As a functioning part of the team he had served for decades before and continued to serve for years after being allegedly overruled on the matter of staying in force in Iraq, the systematic effect of his actions is quite different from the idealistic professions of the various members of that crew. Call my cynical and crazy but I think they achieved what they set out to achieve, and a lot of that had to do with setting the potential for democracy as far back as they could manage, overseas and abroad, and advancing the interest of global plutocracy both here and abroad.
) not that Iraq was in any way responsible for 9/11 in the first place.