Will company refuse to hire me for no reference?

I went to an agency today and I gave them a reference from an employer and he said he will contact him today. He told me he would like me to give him another reference but I am not sure who to give him. He asked me when I can give him the reference and I told him tomorrow. This company makes their money by placing people in jobs. Will this agency not hire me just because I don't give another reference? If I want to get hired should I make sure to give a reference or shouldn't it matter?