This is more opinion on my part since I don’t know if there is a definitive answer.
That being said: A long time, if it EVER happens.
Airliners today are very automated, and many can land themselves. In fact, for the lowest-visibility landings an auto-land is required (the notable exception being the NG 737 with a HUD, where hand-flown Cat III approaches are done). However, this does not mean the airliners can do everything themselves.
Often the most difficult part of a flight is negotiating the taxiways at a busy airport. La Guardia and O-Hare are particularly fun at night and in the rain. How does an “auto-taxier” do this? You could embed transmitters in the taxiways and sensors in the nosewheels, keeping the aircraft on centerline. You would also need auto-throttles and autobrakes that work on the ground. These would have to operate verrry smoothly to get the results you have today. It could be done, but it would be very expensive. You would also essentially cede all control on the ground to the ATC folks, because they would issue instructions to the computers on the airplanes who would then follow the assigned taxi route. If controller one tells Airliner X to cross runway 17R while controller two issues a landing clearance to Airliner Y for the same runway, what happens?
The airplanes would also need sensing equipment to detect other airplanes taxiing around. Just because Low-Cost airways eliminates the pilots doesn’t mean that their won’t be ANY pilots out there. Pleasure pilots will still fly, and they won’t be installing any of the fancy “tracking” equipment that does something that they can do themselves. You now have to separate fully automated airplanes from pilots flying for joy of it.
Once you get airborne, who decides which way to deviate around the inevitable thunderstorms? Who decides that the ride is too bumpy and climbs or descends to a smoother alititude? When the (also inevitable) traffic jams happen, who programs the airplanes to enter holding patterns? The controllers again?
What happens when something goes wrong? I’ve had passengers have heart attacks in flight. Who decides when to divert and where you are going? These kind of decisions are dynamic and need a human involved at some point. If the human is not on-scene (in the airplane) you incur some delay. That delay could be critical for the passenger.
As for mechanical failures, most can be dealt with by a sophisticated enough computer, but there are ALWAYS the ones that no one ever though of. Before Capt Al Haynes brought his DC-10 into Sioux City, IA everyone had said that you could NEVER lose all 3 hydraulic systems on that airplane. They did, and then they flew it down using asymmetric thrust from the two working engines.
But all of these technical issues still miss the biggest barrier to this ever happening: who’s going to fly on these airliners? Millions of people are afraid to fly today. How many are willing to fly across the Atlantic with only a computer guiding them? Computers can (and do) fail. Anyone who has ever seen a “Blue screen of death” or who still has “12:00” flashing on their VCR will have a tough time climbing aboard a fully automated airliner.
So, my opinion is that this will not happen for a very long time. Two generations would be my earliest guess, and that assumes that it ever happens at all.
And yes, I know that my job depends on this NOT happening, but I hope that I’ve not let that cloud the discussion.