Mavericks update broke keyboard shortcut for switching Spaces
I actually figured out how to fix this on the fly. 

I believe this state occurs when you inadvertently make a swipe gesture while a ctrl-key is held down. I can't be sure of that, but the fix is to do exactly that: hold down the ctrl-key, and then do the desktop-switching swipe gesture (for me it is 3-finger swipe left or right). 

I don't know how to prevent it from happening, but it's so quick to fix that it has become a non-issue for me.