Like it or not, Mike Tannenbaum has not been afraid in the past to move up in the first round to grab a player he really likes. How high could the Jets go this year? We can get an estimate using Draft Countdown's value chart. Value charts came into vogue a while back as teams assigned a value for each pick in the Draft for the purposes of knowing what makes for a fair trade. It is more art than science, but it can give us a look.
The Jets own the 30th pick of the first round, which is worth 620 points. They do not have a second round pick. Their third round pick is worth 124. Add them up, and the team could package worth 744 points. The 24th pick is 740. Picks past that point are worth less than 50. Picks in future years are worth roughly a pick for a round later this year (ie Jets' first round pick in 2012 is worth the 30th pick of the second round).
Any way you cut it, the Jets would probably have a difficult time moving inside pick 20. A trade up is possible as Tannenbaum has shown few qualms about using later picks as ammo to trade, but do not expect a huge jump to land an elite prospect. Even if the team was willing to move a player, remember how little value players have relative to picks.