Our TCAS II System (speaking from my personal aircraft only) has a lateral range of: 30Nms forwards, 15Nms backwards and 12 Nms to the side. With ETCAS on this boosts out to 60Nms forwards. Vertically in above or below we are looking at up to 7700ft, but in ETCAS this goes out to 12000ft.
As for the question of how sh*tscared would the virgin and delta pilots be, when you consider that the box is taking its height to be where it is in space, and not the highest point on the aircraft, and the tail height of a 767 is 55ft, and the lowest point of the fuselage of a 747 is roughly 25ft below the avionics bay, when the TCAS shows 100ft the aircraft could possibly be only 20 ft apart vertically. If you disregard the fact that they were 1.5Nms apart laterally, its bloody close!!