1. A method for a configured computing system of a program execution service to dynamically modify program execution capacity for users, the method comprising: under control of the configured computing system of the program execution service, the program execution service providing a plurality of computing nodes that are configurable to execute programs of a plurality of remote users, and for each of multiple of the users, receiving information from the user that specifies an initial desired quantity of computing nodes for use in executing an indicated program of the user and that specifies one or more quantity modification triggers for use in later initiating automated modifications to the desired computing node quantity, each of the quantity modification triggers including one or more criteria for use in determining if the quantity modification trigger is satisfied and including a specified computing node quantity change if the quantity modification trigger is satisfied; automatically determining a group of multiple of the plurality of computing nodes for use in executing the indicated program of the user, the multiple computing nodes of the group being of the initial desired computing node quantity, and providing the multiple computing nodes for use by the user at a first time; in response to one or more instructions from the user, initiating execution of a copy of the indicated program on each of the computing nodes of the group, and designating the initial desired computing node quantity as an official computing node quantity that is recorded as being available to the user at the first time; and automatically managing the computing nodes of the group during a period of time from the first time to a later second time, by: during the period of time, automatically monitoring the computing nodes of the group to determine performance characteristics from operation of those computing nodes, and automatically determining that at least one of the quantity modification triggers specified by the user is satisfied based on the determined performance characteristics; during the period of time, receiving at least one instruction that indicates a user-indicated computing node quantity change for computing nodes of the group that is dynamically specified by the user; automatically determining a modified desired computing node quantity at the second time, the modified desired computing node quantity including changes to the desired computing node quantity from the first time based at least in part on the specified computing node quantity changes from the at least one satisfied quantity modification triggers and on the user-indicated computing node quantity change; automatically determining an actual computing node quantity at the second time that reflects a quantity of the computing nodes of the group that are actually available at the second time to execute the program for the user; at the second time, automatically harmonizing the official computing node quantity for the user with the modified desired computing node quantity, the harmonizing including automatically modifying a quantity of the computing nodes that are part of the group by taking actions to change the determined actual computing node quantity to be the modified desired computing node quantity; and providing the modified quantity of computing nodes of the group for use by the user, and designating the modified desired computing node quantity to be the official computing node quantity available to the user at the second time.