Can a prosecutor cross-examine a defendant's Fifth Amendment right?

Defendant complains that this line of questioning was directed at eliciting the irrelevant fact that, at a pretrial hearing, he claimed he had exercised his constitutional rights not to talk with police unless a lawyer was present. Citing Fletcher v. Weir (1982) 455 U.S. 603, 102 S.Ct. 1309, 71 L.Ed.2d 490 and Doyle v. Ohio (1976) 426 U.S. 610, 617-620, 96 S.Ct. 2240, 49 L.Ed.2d 91, defendant urges that this cross-examination violated his Fifth Amendment rights. Defendant further contends that counsel's objection at the outset of the line of questioning (on the ground that the prosecutor was misstating the evidence) sufficiently preserved the issue for appellate review, and any further objection would have been futile because the trial court had already refused to admonish the jury. Moreover, according to defendant, the prosecutor's asserted misconduct was of such a serious nature that an admonition would not have cured the resulting harm.