From TFA, it seems that Carmack believes it would be hard to get the necessary performance without using the NVidia drivers. It's somewhat surprising to me if it wouldn't be possible to get it running acceptably on anything else, even if the game does use a lot of advanced features - but if Carmack says so!
Well, if it absolutely requires new OpenGL features / extensions chances are they aren't present in mesa (on which all open-source drivers are based) yet. So if he's coding for OpenGL 3.1 plus maybe even a couple extensions (for example geometry shaders which are only core GL in 3.2) then currently it wouldn't run certainly. That said, this certainly shouldn't stop id from doing a port. First, the open source drivers never really achieved the performance of the closed ones (though glsl made things worse), so that's nothing new, and some people were (and still are) quite willing to use the binary drivers. Plus, this might actually help to implement these features - if no app uses them anyway, particularly people working in their free time on the open source drivers probably don't see much reason to do any work on them. Can't blame him though that the business case for a linux port might just be not there, that's not really his fault.
Only through hard work and perseverance can one truly suffer.