This paper presents a general framework for the integration of speaker and speech recognizers. The framework poses the problem of combining speech and speaker recognizers as the joint maximization of the a posteriori probability of the word sequence and speaker given the observed utterance. It is shown that the posteriori probability can be expressed as the product of four terms: a likelihood score from a speaker-independent speech recognizer, the (normalized) likelihood score of a text-dependent speaker recognizer, the likelihood of a speaker-dependent statistical language model, and the prior probability of the speaker. Efficient search strategies are discussed, with a particular focus on the problem of recognizing and verifying name-based identity claims over very large populations (e.g., ”My name is John Doe”). The efficient search approach uses a speaker-independent recognizer to first generate a list of top hypotheses, followed by a resorting of this list based on the combined score of the four terms discussed above. Experimental results on an over-the-telephone speech recognition task show a 34% reduction in the error rate where the test-set consists of users speaking their first and last name from a grammar covering 1 million unique persons.