I looked at the last 20 years (except 1994 - nfl site glitch), and apparently it's not out of the norm for the lowest team to be under 10 TD passes. In about half the years the bottom team had nine or fewer, and the worst are shown below.
I would still like to improve our numbers, though.
In 2006, the Raiders had only 7 TD passes.
In 2000, the Bengals had only 6 TD passes.
In 1998, the Eagles had only 7 TD passes.
In 1995, the Buccaneers had only 5 TD passes.
In 1993, the Bears had only 7 TD passes.
My ancestors fought cave bears so I could make this post.