1. A system for providing low-latency computational capacity from a virtual compute fleet, the system comprising: an electronic data store configured to store at least a program code of a user; and a virtual compute system comprising one or more hardware computing devices executing specific computer-executable instructions, said virtual compute system in communication with the electronic data store, and configured to at least: maintain a plurality of virtual machine instances on one or more physical computing devices, wherein the plurality of virtual machine instances comprise a warming pool comprising virtual machine instances having one or more software components loaded thereon and waiting to be assigned to a user, and an active pool comprising virtual machine instances currently assigned to one or more users; receive a request to execute a program code associated with a particular user on the virtual compute system, the program code associated with configuration data for interfacing with a virtual private cloud; determine whether the active pool contains a preconfigured virtual machine instance that is assigned to the user and is configured to interface with the virtual private cloud; in response to determining that the active pool contains a preconfigured virtual machine instance that is assigned to the user and that is configured to interface with the virtual private cloud, assign the preconfigured virtual machine instance to serve as a configured virtual machine instance; in response to determining that the active pool does not contain the preconfigured virtual machine instance that is assigned to the user and that is configured to interface with the virtual private cloud: select an available virtual machine instance from the warming pool to serve as the configured virtual machine instance; and configure the available virtual machine instance according to the configuration data associated with the program code to enable the program code to interface with the virtual private cloud during execution of the program code; acquire a container in the configured virtual machine instance and assign the container to handle the request to execute the program code on the virtual compute system; and cause the program code associated with the particular user to be loaded from the electronic data store onto the container and executed in the container.