This kind of stuff happens all day, every day, at every one of the major border crossings.
You'd be denied entry and that would be the end of it.
"I might end up waiting weeks or months, though."
The American embassy will tell you there's nothing they can do, and you'd be waiting in perpetuity in a hotel on the American side of the border.
The thing is, you may not have such 'rights', at least not in a legal sense. I suggest the duderinos at the border are well aware of what they can, and cannot do.
If you have a beef, it's with Homeland Security or Congress, not the border guy.
And if you're entering a foreign country ... well, your legal rights are pretty thin. So there's that.
PR Storm? This is the first I've read about it, and it's the NY Times. I don't see anything relating to it on CBC, Globe or National Post sites. Nothing on CBC Radio 1 in my drive to or from work, either.
You'd be waiting forever.