Demps attended South Lake High School in Groveland, Florida, where he was a second-team Class 4A all-state selection at running back, gaining 1,401 yards on the ground, along with 16 touchdowns on 157 carries during his senior year. As a junior, he rushed for 21 touchdowns and 1,761 yards on 170 carries, earning second-team all-state Class 3A selection honors. Regarded as a four-star recruit by Rivals.com, Demps was listed as the No. 36 football prospect from the state of Florida in 2008.
In track, he ran the 100 meters at the Florida state final, the fastest time recorded at that event at 10.37 seconds. He also clocked a 10.25 at the AAU Junior Olympics, the second-fastest time ever in the state and the fastest clocking recorded by a high school senior that year. Competing at the 2008 U.S. Olympic trials, Demps set a new national high school record with 10.01 seconds, beating J-Mee Samuels' 10.08 seconds. His time also equaled the 100 meters world junior record, originally established by Darrel Brown in 2003.
In 2009, Demps competed in four outdoor meets for the Gators track and field team. He ran the anchor leg of Florida’s SEC Championship 4×100m relay team (alongside Jeremy Hall, Calvin Smith, Jr., and Terrell Wilks), which recorded the third-fastest time in school history (38.74) and won Florida's first the 4×100-meter relay title since the 2004 season. Following an injury, Demps only ran a 10.30 over 100 meters at the SEC Championships, placing him ninth overall. At the War Eagle Invitational, Demps helped the Gators win the 4×100-meter relay.
In March 2010, Demps won the 60 meters in 6.56 sec at the 2010 NCAA Indoor Track and Field Championships in Fayetteville, Arkansas. Three months later at the NCAA Outdoor Track and Field Championships, he beat favored Rondell Sorrillo by a margin of .13 seconds, claiming the school’s first 100-meter NCAA title since Bernard Williams won in 2000. Demps' time of 9.96 would have been a new school record had the race not been heavily wind-aided (+2.5 m/s). He claimed the 2012 NCAA Indoor title over 60 meters with a personal best run of 6.52 in the heats, then time of 6.56 seconds to win the final. At the 85th Texas Relays in March 2012, Demps won the 100 metres in the university group, ahead of Aaron Ernest of LSU.
On July 25, 2012, Demps was added to the 2012 U.S. Olympic roster as a member of the 4×100 meter relay pool, serving as a replacement for Mike Rodgers, who suffered a stress fracture in his left foot. He raced the first leg of the preliminary second heat and helped the U.S. 4×100 relay team achieve a time of the 37.38 seconds, which was the fastest time of the preliminary round and broke a 20-year-old American record. The team would go on to win a silver medal in the final round with Tyson Gay and Ryan Bailey instead of Demps and preliminary teammate Darvis Patton, but as part of the team, Demps still received a medal. The medal was later stripped, after Gay failed a drug test.
Demps skipped the 2012 NFL Combine and Draft in favor of preparing for the 2012 Summer Olympics. However, he attracted interest from NFL teams after the Olympics, and agreed to terms on a three-year deal with the New England Patriots on August 17, 2012. On August 31, 2012, he was placed on injured reserve and thus missed the entire 2012 season.
On April 27, 2013, the Patriots traded Demps to the Tampa Bay Buccaneers along with a seventh-round selection (229th overall) in the 2013 NFL Draft for running back LeGarrette Blount. Demps was released by the Buccaneers on August 30, 2014 as part of the final roster cuts. On August 31, 2014, Jeff Demps was signed to the Bucs practice squad.