There are a number of ways denial of counsel of choice can come up, most frequently related to the availability of civilian counsel. Here’s an interesting one.
United States v. Gonzalez-Lopez, 548 U.S. 140 (2006). The opinion is written by Justice Scalia. Here are the important part of the opinion:
In sum, the right at stake here is the right to counsel of choice, not the right to a fair trial; and that right was violated because the deprivation of counsel was erroneous. No additional showing of prejudice is required to make the violation "complete."
United States v. Gonzalez-Lopez, 548 U.S. 140, 146 (2006).
There is no harmless error analysis, it is a required reversal.
The right to select counsel of one’s choice, by contrast, has never been derived from the Sixth Amendment’s purpose of ensuring a fair trial. It has been regarded as the root meaning of the constitutional guarantee. See Wheat, 486 U.S., at 159, 108 S. Ct. 1692, 100 L. Ed. 2d 140; Andersen v. Treat, 172 U.S. 24, 19 S. Ct. 67, 43 L. Ed. 351 (1898). See generally W. Beaney, The Right to Counsel in American Courts 18-24, 27-33 (1955). Cf. Powell, supra, at 53, 53 S. Ct. 55, 77 L. Ed. 158. Where the right to be assisted by counsel of one’s choice is wrongly denied, therefore, it is unnecessary to conduct an ineffectiveness or prejudice inquiry to establish a Sixth Amendment violation. Deprivation of the right is "complete" when the defendant is erroneously prevented from being represented by the lawyer he wants, regardless of the quality of the representation he received. To argue otherwise is to confuse the right to counsel of choice–which is the right to a particular lawyer regardless of comparative effectiveness–with the right to effective counsel–which imposes a baseline requirement of competence on whatever lawyer is chosen or appointed.
Gonzalez-Lopez, 548 U.S. at 147–48.
There is of course a dissent.
Within the military there is no hard and fast rule, and there are certainly cases supporting a denial of civilian, military, or IMC. But, I make these my starting point.
The right to counsel is fundamental to our system of justice. It should therefore be an unusual case, balancing all the factors involved, when the judge denies an initial and timely request for a continuance in order to obtain civilian counsel, particularly after the judge has criticized appointed military counsel. Indeed, we have noted that the right to civilian counsel is a "most valuable right," and that therefore a continuance should be granted at least after initial requests for such counsel have been made, and certainly in a case where Appellant is unsure of his appointed military representation. Accordingly, we hold that the MJ erred by exercising an inelastic attitude in rescheduling Appellant’s trial, where such request was predicated on judge’s negative comments about Appellant’s original military counsel and Appellant’s subsequent selection of a new civilian counsel.
United States v. Wiest, 59 M.J. 276, 278 (C.A.A.F. 2004)(citations omitted).
Where a MJ denies a continuance request made for the purpose of obtaining civilian counsel, prejudice to the accused is likely.
United States v. Miller, 47 M.J. 352, 359 (C.A.A.F. 1997).