The way that the BDR's are created it take into account fuel stops. Unless you drive a vehicle that has a small tank and gets really bad mileage, you should have no issues doing the sections with no extra fuel. Each section is +/- 100 miles. Most are less than 100 miles.
I completed the WABDR last year, it was awesome. I have done the lower sections several times, but only end to end once.
I'd be willing to do the WABDR again.
We just finished the Idaho BDR. It is broken down into eight sections. Here it is broken down by section according to their paper map:
1 - 174 miles
2 - 200 miles
3 - 205 miles
4 - 125 miles
5 - 190 miles
6 - 127 miles
7 - 106 miles
8 - 110 miles (and once we got to the end, I'm trying to remember if there was gas nearby. We drove to Bonner's Ferry for lunch and there was gas there).
Link to our IDBDR trip -
US Northwest - Idaho BDR (and then some!) | OVERLAND BOUND COMMUNITY
My TJ has a highway range of a little over 200 miles on a good day (technically it should do about 250 miles - I've never run it dry). Figure less range when overlanding and pulling a trailer. More than once on the IDBDR sometime at a convenient time during the day when the gauge was getting close to a quarter tank I poured my Jerry can's contents into the tank as a precaution before getting to the next gas station (and then of course refilled it when eventually getting gas at a station). Of those Jerry can times, maybe only once do I think I would have actually run out of gas if I hadn't done so.
Some of the towns on the IDBDR with gas were extremely small. We're talking dirt roads, one pump with just one type of unleaded gas, pay inside, and not open all day. It is smart to carry extra gas just-in-case - at least for me and my Jeep/trailer combo.
Glamor shot of the Jeep and trailer on the IDBDR: