It has been claimed elsewhere[1], with reference to something said by Ben Krasnow, that the projected Steam console will run Linux. Take it with a grain of salt until you hear something official, but at least, hints can be found.

[1]: http://www.golem.de/news/pc-spielekonsole-steam-box-ohne-win... [german]

edit: For those who don't know golem.de (presumably most here), it is one of the two major respectable German IT-news sites (next to heise.de, translated as The H)