one of the main rules for a Bug out Bike is not to skimp on tyres and tubes and even rim tapes. My Bug out Bicycle is using Schwalbe Marathon Dureme tyres and Slime self healing Tubes with Velox cloth Tapes.
http://www.schwalbetires.com/bike_tires/road_tires/marathon_dureme As well as carrying spare tubes, a folding bead tyre is recommended as well as part of the bicycle repair kit.
The last thing that you would want would be to have to call on Bicycle repair man!
http://www.youtube.com/watch?v=54CpPlCnM4I