A frog in my throat

Having "a frog in my throat" is a common expression referring to the hoarseness of one's voice.

Given the fact that the most famous Muppet character, Kermit, is a frog, the expression has found its way into many productions as a part of a joke.

References

In Julie on Sesame Street, Kermit struggles to make it through the opening lines of "Bein' Green" due to laryngitis. He remarks, "Bet you thought I was gonna do the old joke about having a man in my throat, didn't you?"
In a 1975 appearance on The Tonight Show, Kermit does make the "person in my throat" joke in response to his own. "That's a frog joke, real big with all the frogs out there," he tells Johnny Carson.
In episode 115 of The Muppet Show, Behemoth visits the clinic for his sore throat. Dr. Bob inspects and discovers that Behemoth has a frog in his throat - Kermit, to be exact.
Kermit tells Bob Hope that he's speechless when participating in The Bob Hope All Star Christmas Comedy Special. Hope is surprised and suspects he must have a person in his throat.
Dolly Parton claims to have a frog in her throat before duetting with Kermit on Dolly. She tells him she's only croaking with him.