Does a defendant have a right to access counsel who is not "under a conflict of interest"?

A defendant has a right, under both the federal and state constitutions, to the assistance of counsel who does not labor "'under a conflict of interest that compromise[s] his or her loyalty to the defendant.' [Citation.] 'As a general proposition, such conflicts "embrace all situations in which an attorney's loyalty to, or efforts on behalf of, a client are threatened by his responsibilities to another client or a third person or his own interests. [Citation.]"'" (People v. Doolin (2009) 45 Cal.4th 390, 417.)