[Oberon]

What most basic of Constitutional rights is being trod upon when a policeman asks to look in my briefcase?

None at all, if all he does is ask. Then you can say "No" and go on about your business. If you can't say "No" and go on about your business, then your right to be secure in your person and your effects has just been shot in the head.

[RedRover]

But I have a choice. I can simply not take the subway. If I choose to ride, I will cooperate with the police.