However far his legs will take him remains unknown after the third-round draft pick out of North Carolina State got his first taste of the NFL by attending Buffalo's three-day rookie minicamp that closed Sunday. What's unmistakable is the healthy sense of self-belief Graham carries when providing a simple answer to what the draft experts might have missed in dismissing his potential.
"Me," he said, with a smile, noting how some questioned whether he'd even be drafted at all. "They don't know me."
Bold as the response might be, Graham won't apologize for expressing confidence.
"I've been through a lot," he said. "My family's ups and downs have helped me get to this point, built me."
Graham is referring to how the comfortable life he was accustomed to living as the son of an elite track coach was turned upside-down some seven years ago. That's when his father Trevor Graham's career came to a stunning halt as a result of his connection to the BALCO performance-enhancing drug scandal.
The elder Graham, whose stable of athletes included Marian Jones, has been banned for life from coaching competitive track. In 2008, he was sentenced to a year of home confinement for lying to federal investigators.
It wasn't an easy time for T.J. - Trevor Junior.
He was barely a teenager when the free Nike gear he used to get stopped showing up. Classmates he regarded as friends began distancing themselves. And every time Graham turned on his favorite sports network meant the possibility of seeing the family name on the ticker.
The scandal didn't change the love and respect Graham had toward his father, except to draw the two - and the entire family - closer.
"He's my role model," Graham said of his father, who was a member of Jamaica's silver-medal-winning 4-by-400m relay team at the 1988 Summer Games.
What did change was Graham's outlook toward his own future.
"Before, being a kid, you kind of just think that you're going to live forever as a kid," said Graham, whose mother also ran track professionally. "That was a point where I realized that one day I'm going to have to have a job and figure out what I want to do.
"The NFL was my dream."
And now he's on the cusp of living it in Buffalo. He's a member of a team with an immediate need for a player with Graham's speed - the Bills timed him at 4.38 seconds in the 40-yard dash - to provide its offense a deep threat opposite starter Stevie Johnson.
Though Graham wasn't ranked high on many draft charts, the Bills were so interested that they traded a seventh-round pick to move up two spots to take him 69th overall.
"Well, the worry was he wouldn't be there," general manager Buddy Nix said. "You just don't want to get that close and not get him."
Graham is regarded as a raw project after a four-year career at N.C. State, in which he was a full-time starter in only his senior season. He finished with 99 catches for 1,453 yards and 12 touchdowns in 46 games. Graham made a bigger impact on special teams, setting the ACC record with 3,153 career kickoff return yards.
His lack of experience at receiver leaves open questions of how quickly he'll be ready for the NFL.
"He's not polished," coach Chan Gailey said before noting the player's potential. "With that speed and ability and the attitude he carries to me on the field, if he'd been a three-year (starter), he'd have probably been a little bit higher up the board."
Aware of Graham's history, Gailey is particularly impressed by the player's confidence and drive, the intangibles that can't be measured in draft reports.
"It's the old saying of, `If it doesn't kill you, it makes you stronger,"' Gailey said. "I think he's become a stronger person probably because of all he's been around and been exposed to in life. ... That's hard to deal with, but obviously, he's turned out great."
Graham doesn't shy from discussing his past, though BALCO's not something he considers a conversation starter. To do so, would be to dredge old memories that have nothing to do with his chances of breaking into the Bills lineup.
At the same time, Graham will attest that what he's overcome has better prepared him for what's ahead.
"It helped me get to this point," Graham said. "I think without it, I probably would've just been some average guy. But it's toughened me up, it grew me up a lot faster."