When I first started it was a little unsettling, but these days I completely ignore it. Most of the patients who make these threats are emotional, sick or injured, under the influence of their chemical of choice, or already in custody.
In short, I've accepted it as part of the job. I don't leave the hospital looking over my shoulder.
But then every so often a story like this comes along, in which an ER patient is arrested for making threats against the staff. What catches my attention isn't that somebody would threaten to kill the very ER workers they turn to for help, but that the person is actually arrested for it.
I guess I just forget that in the real world, it isn't acceptable to threaten to kill someone. Go figure.