It all depends on what you feel you would be comfortable with and what you want to carry.
Some folks like to carry a huge amount of stuff (support wagon/truck or not) with handlebar bags, panniers, kitchen sink etc. Check your owners manual for the maximum weight limits on the frame. That includes cargo (like a seatbag etc.) and yourself. Some people also like to have fenders etc.. Most road bikes won't let you mount that sort of stuff.
My own bike for example has a cargo weight limit of 5 pounds (Specialized Roubaix) and that's for a seatbag only. I've got a very small seatbag that has 1 spare tube, a CO2 inflater, a multitool and some tire levers and that weighs about 3 pounds. Aside from water bottles, full carbon road bikes aren't meant to carry stuff, period.
Some road bikes with an alloy frame and a carbon front fork will allow you to mount stuff on the bike.
The GWTA folks don't recommend two things in their FAQ.
http://www.waterfronttrail.org/gwta_...Whatkindofbike
Don't ride with knobby mountain bike tires (you'll be dead on your feet at the end of day so put on slicks instead) and "
Lightweight, narrow tires that can be pumped to a very high pressure are not suitable" ( 700c x 23 road bike tires pumped at 120+ psi will be sliced to ribbons on some sections).
My guess is that you could survive on 700c x 25 or 700c x 28 on a road bike as long as they were something like Specialized Armadillos or Continental Gatorskins.