when I filed my h1 few years ago, my client had no issue issuing me a client letter, but my vendor had some problem (They said you are not our direct employee so we cannot issue you), there was so many back and forth (emails), but finally they had to issue me a  prime vendor letter, 

My client is cool, they issued me client letter twice (without any objection), you have to talk to you HR department or your direct manager and let them know that if  they don't issue a client letter you might get RFE. (it is good if you don't get RFE) however if you do get RFE , then they ultimately has to issue you client letter , that is my understanding

good luck, I know sometimes some people are tough, but there is always a way out :)