1. An interrupt controller comprising: circuitry coupled to one or more devices in a system to receive interrupts from the one or more devices; and an interrupt router coupled to the circuitry, wherein the interrupt router is configured to: select a processor from a plurality of processors in the system for a first interrupt received from one of the devices; signal the first interrupt only to the selected processor from the plurality of processors; initialize a timeout counter to a first timeout value in response to signaling the first interrupt to the selected processor, wherein the first timeout value is one of a plurality of timeout values and is selected responsive to a state of the selected processor, and wherein the state includes whether or not interrupts are enabled in the selected processor, wherein a given timeout value of the plurality of timeout values corresponds to the state in which interrupts are disabled in the selected processor, and wherein the given timeout value is dependent on a typical amount of time that interrupts are disabled in the selected processor; select another processor for the first interrupt responsive to detecting expiration of the timeout counter for the interrupt without a response from the selected processor; and signal the first interrupt to the other processor responsive to selecting the other processor.