Go the distance is a metaphor from boxing that means, when used of a boxer, complete a fight without being knocked out or, when used of a boxing match, last the scheduled length. In the USA there is an additional baseball-related sense : pitch for the entire length of an inning.
1998 - Times - Everyone wants to see an amateur who can go the distance,' another spectator said. Kuchar has certainly gone the distance.
within spitting distance
within a very short distance
1991 - Time - His reputation as a hard-boiled novelist is within spitting distance of Hammett's and Chandler's.