The Collaborative International Dictionary of English v.0.48:

Barnstorm \Barn"storm`\, v. i. & t. [Barn + storm, v.]
   1. To travel from place to place, making brief stops.
      [PJC]

   2. To fly an airplane from place to place, usually at small
      airports, doing flying stunts or flying passengers for
      sightseeing, for the purpose of earning money.
      [PJC]

   3. to tour the country to solicit votes.

   Syn: whistlestop.
        [WordNet 1.5]

WordNet (r) 3.0 (2006):

barnstorm
    v 1: appear at county fairs and carnivals as a stunt flier and
         parachute jumper
    2: tour the country making political speeches, giving lectures,
       or presenting plays; "The presidential candidates are busy
       barnstorming this month"

Moby Thesaurus II by Grady Ward, 1.0:

30 Moby Thesaurus words for "barnstorm":
   act, act as foil, appear, come out, control, copilot, drive, emote,
   emotionalize, fly, get top billing, manipulate, mime, pantomime,
   patter, peel off, perform, pilot, play, play the lead, playact,
   register, sketch, solo, star, steal the show, stooge,
   tread the boards, troupe, upstage