Is that a normal number of leads to have in play? I certainly spewed my fair share of resumes into the void out of school but I haven't done that since.

I don't think so because most of these leads came from frontend recruiters that could have made a lot of money landing me a job, and as a result most of them were great opportunities for the recruiters, not so great for me and the potential future employer.

Don't get discouraged. Work on a personal project if you want, so you have something to show. In my experience it's only hard to land the first job. Once you do, it becomes easier. Don't read other people's experiences and think something is wrong. Good luck <3