And if that button doesn't work...there should be a little loop pull tucked away in front of the passenger door area. About where the carpets meets the dash. FWIW, I've had trouble using that fail-safe pull before (possibly too much slack in the line).
Tip: When you push the glovebox button, have your hand on top of the glovebox ready to pull firmly (but gently) towards the seat. Try to time your pull to a split-second after you hear the mechanism activate. Also, it could be that the catch/latch is out of adjustment. Have a look at it when you do finally get it open.