Scientific American's 60-Second Psych podcast points out an interesting study from the academic journal Reading and Writing that shows that texting / SMSing does not have any impact on spelling ability. Indeed, apparently those who spell well in standard English spell well in "textese".
When I posted this link on Facebook, I got a couple of queries on whether the results worked for those for whom English is not a first language. I don't know, but it seems that the same complaint on "textese" apparently affecting spelling is common in environments where English is the primary language, which is probably why there was even interest in the experiment. So I would certainly not rule out the idea that something other than "textese" is affecting standards of spelling, and that there is some confusion of correlation and causation. Another possible cause, for example, could be a general reduction in the value that society as a whole places on spelling, perhaps because of the existence of easily available spell-checking and the like, causing students growing up in such a society to not care about spelling.
Also found this interesting story about another study on SMSs and language.