In my experiences a SC of 2 hours is rare. Usually it's 6 or 8 hours or sometimes more (although it has been a few years since I sat RSV) OR it's 45 minutes... In which case the scheduler has always asked "When can you safely get to the airport so I can let Crew Tracking know? Please be safe, we'll see you in X amount of time."
Same goes for short notice GSs. I have learned over the years that when they are calling that late in the game the flight is already late and DAL is just trying salvage a flight instead of cancelling it. If you are 15 minutes later than you 'could have been' because you took a few extra minutes to drive the speed limit the airline isn't going to grind to a halt.
Also, as has been said, don't abuse the fact that SC is not specifically defined!