No, there is no object of "have". "have to" is an idiomatic combination meaning "be forced/obliged to". "How many times" is adverbial.
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teechrIt is an object of "tell."I'm afraid I can't see that. "How many times" refers to the frequency with which "I have to tell you" occurs.
GPYI'm afraid I can't see that. "How many times" refers to the frequency with which "I have to tell you" occurs.I agree.
contraposition How many times do I have to tell you?Is 'how many times' the object of 'have'?By the way, an example of a superficially similar-looking sentence with that sort of structure would be: