In two cases over a half-century ago (McNabb and Mallory), the Supreme Court gave teeth to the prompt presentment rule (see Rule 5(a)), holding that any confessions made during a delay in presentment must be suppressed. Congress codified the holdings at 18 USC 3501(c), drawing a line at the 6-hour mark. In other words, any confession made by a defendant more than six hours after arrest is inadmissible if the defendant has not been "presented" to a judge (think initial appearance). The time limit is somewhat flexible (depending on distance and difficulty to the nearest judge).
Despite the rule's age, this recent Third Circuit decision is a great reminder that the rule is not always followed. There, officers interrogated the defendant past the 6-hour mark and prior to his initial appearance. The district court admitted the statements at trial, the jury returned a guilty verdict, and the court imposed a really long sentence (over 24 years). The Third Circuit reversed. It rejected the government's argument that the defendant's attempts to cooperate justified the delay. It mentioned, among other things, that "the longer a defendant goes without being apprised of his rights, the more vulnerable he is." It also discussed the problem with false confessions. It is a great read, and we encourage you to read it. You can also read more about the case here.
So, remember to check the time-stamp on any pre-presentment statements made by your client. If the statements were made more than six hours after arrest, you might have a colorable argument to suppress the statements.