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                           general:: 
                            Phrase(s): have someone on the string 
Fig. to have someone waiting for a decision.  •  Sally has John on the string. He has asked her to marry him, but she hasn’t replied yet.  •  Yes, it sounds like she has him on the string.
                        
                        
 
                        
                            McGrawhill's American Idioms And Phrasal Verbs