Now that Mark Sanchez has been released and Michael Vick has been signed, I think it's appropriate to update everyone with where the team stands, salary cap-wise. Before these moves, the team stood at roughly $23.9M. The release of Sanchez freed up $8.3M in space, and Vick cost $5M. That leaves $27.2M in cap space. Once you take out the expected cost of the rookie draft class, the New York Jets have approximately $25.2M remaining. Including draft classes, the only teams with more space are the Cleveland Browns and the Cincinnati Bengals, and it's a negligible difference.
Since many are curious about DeSean Jackson, it's worth noting that his contract would cost approximately $10.5M in cap space. There aren't a whole lot of teams left that can afford such a contract, plus their draft classes, plus projected in-season spending. The New England Patriots would have to release Vince Wilfork, and even then, there wouldn't be a lot of space for their draft class and in-season spending, although they can certainly make it work if they want. The Carolina Panthers are all but out of the question with just a little bit of space remaining. Ultimately, if the Philadelphia Eagles really want to deal Jackson, the Jets are likely their best option with a considerable amount of salary cap space and the requisite number of picks.
However, with re-signing Muhammad Wilkerson, Jeremy Kerley, Damon Harrison, etc., on the horizon, the team should have plenty of money to make things work, regardless of how the potential Jackson trade works out.