Depends on the seller though. eBay "Like New" is just a label anyone can slap on. Did you check their feedback before buying? Most refurbishers offer at least a 30 day warranty on electronics. If they didn't, that's a red flag right there.
Oh man, you're missing the biggest thing... refurbished stuff often has a different serial number or hidden cosmetic damage that "Like New" doesn't cover, and that's what really screws you down the line.
Did you actually check what their return policy said before you bought though @harper914? I mean, I've found that some refurbishers will fight you on any tiny scratch they claim isn't covered, even if the listing said "like new." It's a real headache if you don't screenshot the original listing details right away.