I think your question got cut off. The first part of the question has a character limit, but you can add more information in the area below that is not in bold type.
Can I mount tile to sheetrock or does it have to be cement backer board?
You should be able to mount it to the drywall for a small counter backsplash. Here is a thread with some more opinions, but this is about a backsplash for a shower, so there is more concern about water in this case:
Steve, a backsplash in an area that is not continuously soaked with water can be directly applied to the existing (undamaged) drywall. "Acrylpro" mastic is a great choice for this. Home depot sells it, low odor and easy clean-up too.
Steve...drywall is fine for a backsplash...and the Acrylpro that Imagery mentioned is some nice stuff to work with. I like to use it for all applications short of showers. Check out this article I wrote of backsplashes...it may give you some ideas.
Thanks to all for your advice. Now I have to get back to work!!