Oh yes, the button does the scale down animation and the clicking sound. And the near clipping plane is positive 0.3, far is 25 (took the values from the tutorial). The button itself is at Z: -2, and the camera - at Z: -10. And they all look pretty far from each other in 3D view.
UPDATE: it works now. I just dragged the same object to the Target field (under 'Send Message' in the inspector) and simply picked the method from the list. Object sending message to itself. Still wondering why the code approach didn't work, but everything is fine now.
Thanks again!