The only clue I had to be anticipating something was amiss was a "rubbing/thumping" sound as I started up from a traffic light or two. The frequency increased and then went away at speed. I was doing about 65 down a highway when the rubber pieces on my flex disc started leaving the scene. The sound of bits slamming against the tunnel was startling and I saw chunks of rubber hopping all over the roadway in the rear-view mirror. I was at a constant speed and only four corners from home, so I made it there, very gently, on the remaining cords.
If your sound is coming from the transmission/driveshaft tunnel, I would not drive the car unless your repair shop is very close, and be very, very gentle with the clutch. Just have them put it on a lift and look. If you see white cords, park it until repair.
If you do it yourself, there are good threads here about the details involved.
Ray
'68 280SL 4-spd Coupe