I've done all my tours on a department store bike (Schwinn). Never really a problem outside the normal stuff like flats, and a lose bolt. I always mod the bike a little bit, putting on steel pedals instead of those cheap pedals. I use one of those Wald back racks with the steel panniers already attached. Gives me a wide space a million ways to attach stuff. Never a major mechanical problem.
You can tour on anything, but what I will say is you need a bike that comfortable to ride day in and day out. If your bike isn't comfortable, touring is hell and not fun.