Spencer was born in Paterson, New Jersey (although some sources say New York City) and grew up in nearby Totowa, the son of blue-collar parents, an Irish American father and an Ukrainian-American mother.[1] With his enrollment at the Professional Children's School in Manhattan at age 16, he found himself sharing classes with fellow students including Liza Minnelli and violinist Pinchas Zukerman. Later he attended Fairleigh Dickinson University but did not complete a degree.

Spencer began his television career on The Patty Duke Show. He played Harrison Ford's detective sidekick in the 1990 courtroom thriller Presumed Innocent. In the early 1990s, he was a regular cast member on L.A. Law, playing the rumpled, pugnacious associate attorney Tommy Mullaney. Later, he acted in the romantic comedy Forget Paris (1995) as a wisecracking co-worker to Billy Crystal's basketball referee; The Rock (1996) as the weasely FBI official Womack, and the 2002 theatre production of The Exonerated. Paralleling his character on The West Wing, he was a recovering alcoholic and divorcee. Spencer was actually the first actor cast in the West Wing.

Spencer won an Obie Award for the 1981 off-Broadway production of "Still Life," about a Vietnam veteran, and received a Drama Desk nomination for "The Day Room." After two previous nominations, Spencer won his first Emmy Award in 2002 for Outstanding Supporting Actor in a Drama Series for his portrayal of Leo McGarry on The West Wing. The episodes Spencer submitted for judging by the Emmy voters were "Bartlet for America", in which Leo has to testify in front of a Congressional committee about the President's health and flashes back to his own medical lapse, and "We Killed Yamamoto".

Spencer died following a heart attack in a Los Angeles hospital on December 16, 2005, four days before what would have been his fifty-ninth birthday. West Wing cast mate Stockard Channing was visiting with Spencer at the time of his death. He was buried in Laurel Grove Memorial Park in Totowa, New Jersey. [1] At the time of his death, Spencer had appeared in two of the five West Wing episodes then in post-production. Those episodes were Running Mates and The Cold. His death was subsequently written into the show as his character, vice presidential candidate McGarry, dying of a heart attack on election night. Coincidentally, the fictional character had a disconcerting history of heart problems.