Not surprisingly, the music industry had absolutely no idea what to make of the band, so TMBG promoted themselves through Dial-A-Song. The group posted ads in local newspapers (such as The Village Voice) with a phone number, which led to an answering machine with a taped song. The band maintained the service even after they were signed; some listeners estimate that more than 500 songs were recorded over the years.
Helped by Dial-A-Song, TMBG generated enough interest to be signed in 1985 and their self-titled debut LP came out the following year. The album even picked up some college radio airplay. 1988's Lincoln actually charted (#89) and "Ana Ng" picked up some mainstream radio airplay as well.
Of course, the band's big break came in 1990 with the Flood album ( "Birdhouse in Your Soul" and "Istanbul (Not Constantinople)" may both be familiar to readers. TMBG's period of major success was relatively brief, but they maintained a loyal following, and expanded their audience in the mid-2000's with a series of children's albums. The band remains active in the industry as of this writing.
Cool trivia fact: At their first concert, They Might Be Giants used the name, El Grupo de Rock and Roll.