David Schramm received his training as a member of the first class taught by famed producer-director John Houseman at Juilliard. Along with fellow graduates, including Kevin Kline, Patti LuPone and David Ogden Stiers, Schramm was a founding member of The Acting Company, which toured the US. Houseman later picked the actor to play "King Lear" in an Off-Broadway production of the Shakespeare classic. Schramm made his debut on Broadway in "Bedroom Farce", with John Lithgow.

His early TV work including a limited role as a doctor on the NBC daytime drama "Another World". In 1983, Schramm was cast as secretary of defense Robert McNamara in the biographical miniseries "Kennedy" (NBC, 1983). But Schramm remained relatively obscure until 1988 when he appeared at the Pasadena Playhouse opposite Rebecca DeMornay in a production of "Born Yesterday". He then began to receive TV offers, and guest starred on episodes of "Wiseguy" and "Jake and the Fatman," as well as playing supporting roles in the feature films "Let It Ride" and "Johnny Handsome" (both 1989). In 1990, he played the recurring role of the police captain on the short-lived CBS series "Max Monroe: Loose Cannon" and the father of Tess McGill (Sandra Bullock) on the 1990 NBC series version of "Working Girl". A supporting role in the 1990 NBC TV-movie "Dreamer of Oz: The L. Frank Baum Story" brought him to the further attention of the network, and he was slotted onto "Wings" for the show's premiere.