Not much, or at least not much of any great consequence. You already mentioned that there is reason to believe we could have detained and possibly deported a few of them (although it's unstated that this would have amounted to a much more involved, comprehensive INS sweep than just picking out a few key individuals, who weren't especially distinguishable from the illegal masses). However, there is little reason to think that this would have prevented the eventual attacks.
Do you really think that banning fingernail clippers at that time would have stopped the attacks?
No. As a matter of fact, my personal opinion is that the only thing that is much likely to prevent comparable attacks at this time is that passengers are now likely to resist and seize or crash the plane.
...do you think the administration would have been able to overcome the bureaucratic inertia and change things before an attack occurred?
Certainly not. One of the key reasons being that there was simply not that much apparent cause for alarm. That's a somewhat cold statement in hindsight, but the fact of the matter is that no one envisioned that the World Trade Center towers would collapse. I mean, it still would have been an ugly event if planes crashed into the buildings, but we are talking about several lower orders of magnitude than what actually ended up happening.
The WTC buildings were designed to remain standing in the event of a plane crash. Everyone who had examined the matter knew that. Some have said that the buildings should have been evacuated immediately but even John O'Neill, the former head of FBI counterterrorism - who was then head of WTC security - did not see fit to order an evacuation on 9/11.
While it was no shock to people long familiar with Al Qaeda's tactics and objectives, it is nonetheless true that a lot of things unfortunately came together just right for them to pull off what actually happened and wreak the level of destruction that they did.
In hindsight, it's easier to just say that no one could have imagined they might fly planes into buildings, even though people certainly did and had concrete evidence to expect just that (as linked above).