Problem shrinking Arduino project to ATtiny 85 20MHz

I suggest you to confirm your steps with http://arduino.cc/en/Tutorial/ArduinoISP and https://www.sparkfun.com/tutorials/200 to be sure. It seems you didn't upload Arduino ISP code to your Arduino first. Plug your Arduino to your computer and upload ArduinoISP from Examples menu. Then you may retry to program your Attiny by selecting "Arduino as ISP" from Tools | Programmer menu.