SB Nation's Bleeding Green Nation has an interesting report on how many coaches each NFL team employs. The Jets have 20.
As you can see, there doesn't seem to be a strong correlation. There are some playoff teams at the top, middle, and very bottom. Still, I think it's interesting that some teams opt for less coaches when there's no limit as to how many can be hired (that is, except for the owner's willingness to pay). Perhaps those teams feel it's "too many chefs in the kitchen." Or perhaps they're more sensitive about their coaching staff being poached. While those seem like valid reasons, the benefits of having a large staff include increasing the changes of finding coaching gems. Not to mention the extra assistance during drills and such.
For reference, seven other teams also have 20 coaches. It puts the Jets just on the lower half of the league. The Eagles and the Seahawks have the most with 25. The Steelers have the least with 16. Click the link to see the total results.