Born in Ogden, Utah, Stallings earned degrees from Weber State College, Utah State University and Colorado College. Beginning in 1969, Stallings taught history at Ricks College in Rexburg, Idaho.
Idaho Democrats nominated Stallings to challenge four-term Republican incumbent George Hansen in 1982, but he lost in the general election. In 1984, after Hansen was censured by the House of Representatives, Stallings defeated him in a hotly contested race by fewer than 200 votes. Despite representing a heavily Republican district, Stallings was re-elected three times by comfortable margins.
A conservative Democrat, Stallings unexpectedly won three votes for the presidential nomination from pro-life delegates at the 1988 Democratic National Convention.
Stallings was the Democratic nominee in 1992 for an open seat in the United States Senate, but lost to Dirk Kempthorne, the popular two-term mayor of Boise.
In 1993, Stallings was appointed United States Nuclear Waste Negotiator by President Bill Clinton and served in that capacity until the office was eliminated in early 1995.
Stallings attempted to win his old House seat back in 1998, but was defeated by Mike Simpson of Blackfoot in the general election. The seat was open, as three-term incumbent Mike Crapo successfully ran for an open seat in the U.S. Senate.
After leaving Congress, Stallings later served as executive director of the Pocatello Neighborhood Housing Services and later on the Pocatello, Idaho, City Council from 2001 to December 20, 2007.
In 2005, Stallings won election as chairman of the Idaho Democratic Party. Stallings was re-elected state Democratic chair in 2007. Stallings resigned on December 20, 2007.
On March 14, 2014, Stallings filed to run as the Democratic candidate for his old U.S. House seat in Idaho's Second Congressional District. He was the Democratic nominee after the uncontested primary election, but was defeated by Simpson in the general election.