In their attempt to mimic the proof of Fermat's Last Theorem for GL(n), Clozel, Harris, and Taylor, were led to a conjectural analogue of Ihara's lemma -- which is still open for n>2. In this talk we will revisit their conjecture from a more modern point of view, and reformulate it in terms of local Langlands in families, as currently being developed by Emerton and Helm. At the end, we hope to sketch how this can be used to obtain a factorization of completed cohomology for U(2). [The last part is joint work with P. Chojecki.]