Since the console hasn't been out for a year, it would be covered at a minimum from date of manufacture if you have no receipt from an authorized retailer of the product. eBay isn't one.
You can buy a warranty from SquareTrade for something you bought from eBay, if you want to. It's even offered at time of eBay purchase, if I remember.
Though, even if you buy it on eBay, you still have to pony up use tax on the item if you don't pay sales tax on it from eBay.