Shrum was born in Connellsville, Pennsylvania and raised in Los Angeles. He is a graduate of Loyola High School of Los Angeles and Georgetown University (where he was named the outstanding debater at the 1965 national policy debate championship, the NDT). After Georgetown, he went to Harvard Law School.

Shrum began his political career as a speechwriter, first for New York City Mayor John Lindsay, and then for Edmund Muskie. He later worked for George McGovern, and spent nine days on Jimmy Carter's 1976 campaign.

Shrum later worked for Ted Kennedy and wrote the famous speech Kennedy gave at the 1980 Democratic National Convention.

In 1986, Shrum began work as a political consultant, designing campaign advertising and message strategy for Democratic candidates at the presidential, congressional, and gubernatorial levels. He worked for the Dick Gephardt campaign during the 1988 Democratic primaries, including Gephardt's surprise victory in the Iowa caucus, but after Gephardt's defeat, Shrum helped Democratic nominee Michael Dukakis in preparing for his debates against Vice President George Bush. Dukakis lost the general election.

In 1992, Shrum worked for Nebraska Senator Bob Kerrey, who was defeated for the nomination by Bill Clinton.

In 2000, Shrum helped Al Gore beat back a primary challenge from former New Jersey Senator Bill Bradley, and win the Democratic nomination. Gore would win the popular vote in the November general election versus George W. Bush, only to lose the electoral vote.

In 2004, Shrum worked on John Kerry's campaign, guiding him to a victory in the crucial Iowa caucuses and New Hampshire primary, and soon after, the Democratic presidential nomination, only for Kerry to be defeated in the general election by George W. Bush.

Critics often point out a "curse" associated with the presidential campaigns that Shrum has worked on, since he has yet to claim victory for any of his candidates in eight presidential elections.

Since 1985, Shrum has conceived and produced advertising (TV, radio, print) for twenty-six winning U.S. Senate campaigns; eight winning campaigns for Governor; the Mayors of New York, Los Angeles, Chicago, Philadelphia, Denver, Dade County and San Francisco, and the Democratic Leader of the United States House of Representatives. Those winning Senate campaigns include those of Alan Cranston in 1986 and John Edwards in 1998, as well as victories for Barbara Mikulski, Jack Reed, Tom Harkin, Jon Corzine, Harris Wofford, and many others.

In 1994, the year of the "Gingrich revolution," Shrum worked on behalf of two of the few bright spots in a tough year for the Democrats: Chuck Robb's victory over Oliver North in Virginia, and Ted Kennedy beating back a challenge from Mitt Romney. Shrum has also worked for Ehud Barak of Israel and the British Labour Party.