Well some one did port Linux to an AVR processor by adding extra memory in the form of SRAM and an SD card. He got it to run as well. It took 5 hours to boot up to the log in prompt.
Now Linux is a total pain, it destroys any real time operation quicker than 0.1 second but if you want to run Linux for some warped and twisted reason then you can always get a Raspberry Pi. They are available now on next day delivery.