"The thing about it is, you have to climb up," Smith told ESPN.com on Saturday after practice. "If I'm No. 32, by this time next year or the year after, I expect to be in the top 5."
It was a bold statement, considering his struggles through most of last season, but Smith reported to training camp with a greater sense of confidence, according to coaches and teammates. They say he made huge strides in the offseason.
But the league remains skeptical. ESPN polled 26 coaches and personnel executives, asking them to rate this season's 32 projected starting quarterbacks. Smith finished dead last.
He said he is aware of the poll.
"My first reaction was, 'You know, man, I've got to prove them wrong,' " Smith said. "In the end, none of that matters. My key job is to make sure this team is improving and I'm doing everything I can for the betterment of this team."
The Jets are encouraged by Smith's progress, although they haven't named him the starter yet. He's competing against Michael Vick, but Smith, receiving the majority of the first-team reps, is clearly ahead.
Jets coach Rex Ryan won't handicap the race -- he won't even say if Smith will start the first preseason game -- but he clearly believes Smith is on the rise.
"Let's take that survey after the season and see where our quarterback ranks," Ryan told ESPN.com. "Let's see where Geno ranks.
"The beauty of it is, what I know for sure is, we get to prove it. Let's see where we all rank after the season. It'll be interesting to see if they take that survey again, what it would look like at the end of the year."
One of Smith's most ardent supporters is veteran guard Willie Colon. Asked about the ESPN poll, Colon replied: "As far as the ratings, they can stick it.
"Yes, Geno suffered from turnovers [25 last season], but I also remember watching Peyton Manning and some of the other great quarterbacks in their first three years in the league. They weren't lights-out. Over time, they grew into themselves and developed into Hall of Fame quarterbacks."
Colon said Smith has the work ethic required at the position and the mental toughness to handle the never-ending scrutiny. Smith showed resilience last season, emerging from a terrible slump to play well over the final four games.
"He understands he has the weight of the world on his shoulders," Colon said. "To me, that means more than how coaches rank him, because I know him personally and I know what he's all about."
Smith expects to get better with age. Obviously, based on his top-5 prediction, he expects to get a lot better.
"Guys improve all the time," said Smith, who compiled a league-low passer rating of 66.5. "I've been watching football all my life. I've seen Peyton Manning grow up in this league. I've seen Tom Brady grow up in this league. I've seen Drew Brees.
"The main thing with all those guys, they're hard workers and diligent. Those are the things I try to do, too."