I used to have with me a little section of car chammy to dry it off as much as possible, but as others have said, usually if it dry out, having the tent turned upside down and the fly hanging off something while doing the last stuff before leaving is often enough for it to dry. If not, it aint a big deal for the day.
Like others said, if its rainy its going to be wet anyway, and if its a dry day, it will dry out when you set up camp in the afternoon anyway.