767 can't work like the 744 and just tell the a/c what time you want to be there. We need to crunch the numbers ourselves to programme a descent speed which will meet the required time of arrival. We do this by plugging in a mix of cruise and descent speeds which show on the FMC as the required arrival time. With experience you work out that you can lose two minutes by going from a 300 knot descent (which we don't do anymore) to a 250 knot descent. More than that requires a slower cruise speed.
Depending on when they let you know, you can lose up to five or six minutes without too many dramas. Much more than that and the ATCO will have to do some work with vectors.