Imagine that the guy knows his Miranda rights, refuses to talk and demands a lawyer. The unsaid implication of the supposed public-safety exception is that the police will do anything to get the guy to talk, constitution be damned.
No it isn't, because it would be a huge gift to the defense counsel who would rightly attack any infringement of his civil liberties (eg if they beat him up or worse). I've heard Alan Dershowitz make such 'ticking time bomb => anything goes' arguments but I think they're fatally flawed, both legally and logically.