Whatever caused the search length this year, I'm sure it wasn't hugely impacted by Kelly's salary budget being insufficient. I suspect it was more a case of guys deciding where they wanted to coach (i.e. pros/college, another coach/system they prefer, perhaps location, etc) rather than ND not offering enough.
Rees was put in the OC job because that is what Kelly wanted to do, not because he was easy on the budget. And lots of teams take long periods of time to fill assistant coaching roles. Heck, the Packers still do not have a WR coach. Hiring assistants in college can get squirrelly in January particularly since prior connections play a big part and 1) there are new coaches looking to build new staffs and 2) other coaches are locked down until after signing day.