I got a very prompt and very apologetic response (even though I sent the email in the evening), as well as an offer to reship the cup by UPS instead of USPS, two days, or give me a refund. I opted for reshipping, because tampons are torture for me and the response I got makes me perfectly willing to continue doing business with them. In my email, I mentioned the woman who posted here about getting hers in 3 days, and they said that was the normal time it took. If I'm lucky, my period will hold off long enough for the cup to get here before I have to resort to tampons as a temporary measure.
If you consider buying a diva cup from betterlife.com, it's only $19 (with $5 shipping in the USA), and their customer service is very prompt and friendly, even if I was a wimp about emailing them sooner.