Had the same issue last week. My stock, ASUS charger and USB cable would NOT charge the unit whatsoever. I had it plugged in for 14 hours, with the tablet turned off, and 0 charge went into the tablet.
Tried my Galaxy Nexus charger, and it worked, although charged very slowly...took 6 hours to charge it. I also hear a fairly audible crackling noise coming from the USB port on the Nexus when using either charger.
Called up Google, they confirmed the unit was defective. I got my replacement today, just now actually. Haven't opened it up yet.
If you're having problems with the stock charger, there's either an issue with your Nexus or the charger they gave you, and I would advise that ASAP you go and get a replacement device from your point of sale.