OK Guys,
I just figured out that it is something with the boards.txt file or the way the Arduino IDE boatloads. I connected the usbTiny programmer I have to the ATmega328p that I was programming on the breadboard, and I got the same error message as before. It seems as though it is not ArduinoISP, it is the boards.txt file you get from Arduino. I still have not found the problem though, and I even tried in AVRdude. In the Arduino IDE, I was getting the error message "Yikes! Invalid Device signature", but in AVRdude, It read the device signature perfectly. Therefore, I either think something is up with the IDE, or something is up with the boards.txt file.
P.S. I have redownloaded Arduino 1.0 twice already, and this doesn't fix the problem. I am also using a mac, but that should be fine.
Thanks for the recent replies,
Qtechknow