I'm sure Skip will know the real answer, but I don't think you can effectively sue the state for not passing a law.
What legislators fear is not getting re-elected, so you can find yours at:
http://www.gencourt.state.nh.us/whosmyleg/
most of them have email and phone numbers, let them know how their vote will effect your vote.
BTW all the signs I saw had the red circle and slash through the letters HB-162 not the word limits.