Maya and Houdini are available for Linux. The rendering engine for Lightwave is too. I believe XSI is also available. There are also some free 3D apps available for Linux (Wings3D, Blender, Aqsis, Pixie, K3D (though K3D doesn’t look production worthy yet)).
The areas where Linux is currently lacking as far as 3D production are concerned are as follows:
*) No good frame scrubber
*) Audio support is a bit flakey, though better in the 2.6 kernel
*) No good editing solution
*) Available compositors are really expensive.
*) Creating movie files from sequences of still images is a bit clunky.
*) GIMP is annoying to anyone who has used Photoshop extensively before. Crossover Office can be used to run Photoshop under emulation though.
*) ZBrush and 3D paint programs aren’t really available under Linux.
There aren’t any limitations in Linux that prevent 3D apps from being developed for Linux. The biggest thing holding companies back from porting to Linux is that the customer base is pretty small compared to Windows, and they might not make back their porting costs in Linux sales. In time this will likely change.
If you wanted to do 3D production under Linux now, you could. Many movie studios are doing so right now. They just have to write their own software to fill in the missing gaps, or use another platform for certain parts of the pipeline where a good Linux solution doesn’t present itself.