Insect and Spider Identification: Red spider identification help (Nevada), 3 by Snax

Snax wrote:
I came across these bright red spiders 3 or so times in the last few months in Las Vegas, NV. One of them was on my bathroom towel while I was drying myself, and another time I woke up with one on my pillow. Anyway, they don't seem to be very aggressive, but I'm interested to know how dangerous they might be with my close encounters.

The pictures aren't wonderful but it's the best I could do. It's dead in the first three, and kind of curled up.

Thanks.