When you say staffing agency, do you mean a company that placed you in your current or previous job? Best recommendation letters will come from someone that was either your supervisor or is very familiar with your work product that you KNOW will give you a strong recommendation. Schools will ask for your relationship to the recommender, and if it is someone that placed you at a job, it may seem like a conflict of interest b/c technically your acceptance into your new company got them paid. Also, a staffing agent's basic job function is to recommend job applicants for positions, so it may not seem as sincere since they do this every day. You've also never really worked with them in a professional setting (correct me if I'm wrong). I don't know if a staffing agency will have the same credibility as someone you've worked with. If you're young (less than 3 years out of undergrad) and are struggling to find professional recommendations, consider a teacher from your school.
If "staffing agency" means something else, please elaborate. I could be way off.
Anymore information about your specific situation could also help us to give some advice.