I don't pack underwear when touring. I take two pairs of bike shorts and two jerseys and wash them daily if it is convenient, but I really could get by with one set since they wring out well, dry fairly quickly, and I don't mind putting them on damp since they are usually wet from sweat pretty quickly any way.
Also... If I have to go a few days without showering or washing clothes it isn't the end of the world. Daily bathing and daily changing of clothes is a relatively recent cultural development and is not a necessity. Cowboys used to go all winter in the same clothes and were on horseback all day. I get a shower every day when I can, but don't freak when I can't. Some times on the TA we went several days without and didn't contract dreaded diseases, get huge saddle sores, or spontaneously burst into flames. Also I have found that in places where you might have to go a few days without a shower, people tend to be way less prissy about such things, so offense is generally not taken by folks you meet if you are a bit "fragrant".