What they need is to send people into space that are smart enough to understand the myriad systems around the, maintain them, and conduct the various experiments and other tasks planned. Basically, they're looking for smart people that they can train to have the needed skills, rather than people that have the needed skills outright. (Since nobody actually does.)
A pure CS degree might put you at (an overcomeable) disadvantage, since they seem to value the ability to do experimental science. But it can and has been overcome, see:
http://www.jsc.nasa.gov/Bios/htmlbios/chamitoff.html
Also, note that astronauts tend to be selected late in life - mid-30s and early-40s - since NASA likes accomplished people.