Define "touring" bike...
I have seen just about every type of bike ever built used for touring. I routinely tour on a Raleigh 3 speed. Primarily 2-3 days at most. Longer tours I may use a converted hard tail MTB. I even use a Raleigh Twenty for short single night tours (SO24).
Figure out which bicycle style is most comfortable for you, then find one that you can carry what you want/need. Start riding. To me the tour is more about where I go, who and what I see than how I got there and on what.
Aaron