Republican lawmakers said Thursday that Governor Deval Patrick’s health and human services secretary should resign because she did not act with enough urgency in responding to the tainted evidence scandal at a closed state drug lab.

“This isn’t about simply policy differences,” said Representative Bradley H. Jones Jr., the Republican leader from North Reading. “This is about much more than that. This is about moving an agency forward that desperately needs to regain public trust on many, many, fronts and needs to go in a dramatically different direction.”