I've wondered about that. In the context of a police interview, either after being arrested or when you're fairly certain the officer intends to arrest you, the statements "I'd like to speak to an attorney" and "I'd like to speak to my attorney" convey very different things.

The second phrasing says: I have ready access to professional counsel. If you choose to continue with this confrontation, you're the one who's asking for legal trouble. On the other hand, the first one says: I don't know any attorneys, and certainly haven't engaged one. I'm unprepared and scared. I can haz public defender?

Seems like you're always better off trying to bluff.