There's several issues here.

First, remember that only certain individuals are allowed past the checkpoint. Therefore, TSA (or the airport cops for that matter) are entitled to see your boarding pass at any time...and along with that a gov't issued photo ID to "prove" that you are the person who belongs to the boarding pass. So, refusal to show photo ID in connection with your BP *could* be grounds to deny you access to the sterile area.

Now the ol' "can't I just leave?" question. Several of the federal circuit courts of appeals have held (back in the 1970s and early 1980s) that once a person begins the screening process--by walking through the WTMD or placing bags on the belt--they must continue the screening process until it is completed. This presents a grey area depending on the factual circumstances.

As for the local LEO, it depends on state and local laws. As other threads and the recent SCOTUS Hiibel case have shown, different areas have different laws for when you must provide identity (verbally or with tangible ID) to law enforcement. And there are always law enforcement's favorite fallback charges such as "disorderly conduct" or "failure to comply with demands of an officer" or similar equivalents depending on the state.

I'll also take this opportunity to point out that the passport is probably not as much of a "foil" as some on this board present it to be. Remember you gave State your SSN, address, and other info when you applied for that passport. Even if you've moved since you got that passport...between your SSN, your DOB, the address on your tax returns, and post office forwarding records...that's plenty to go on ;-)

Oh...and don't forget the old standby "interference with the screening process."