The current AP software will ask you to touch the wheel periodically to make sure you are still there. And by touch I mean cause a little bit of torque on the wheel.
The time between the car asking you to do so varies and based on my observations, it seems to do it based on the type of road, how defined the lines are, and how fast you are going relative to the speed limit. If you are going the speed limit on a divided highway with nicely painted lines, it may be 5+ minutes without it asking. If you are going 15 over the speed limit and the lines aren't great it will ask you more frequently.
The first warning is just a visual cue on the dash. If you don't touch it after a short period of time it will beep at you as well. If you still don't touch the wheel the car will put the hazard lights on and slowly stop the car. I haven't tested this so I don't know how long after the beep warning it will stop the car, but I've read that it will stop the car right there in the middle of the road (no lane changes or getting off to the side).