Do you know the term "She is a people's person."? I cannot find it in a dictionary. My husband says he knows it from Washington, D.C.
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You would more usually hear:
That is, she is a person who gets along with people well.
The noun "people" is being used as an adjective meaning "effective with/interested in people".
(Although the last two are less common)
I think you (or your husband) might be conflating two different idioms.
"A people person" is someone who gets along well with others and is generally well liked, e.g., "Did you see how Tom handled that irate customer, he is a real people person."
"The people's _" would refer to the popularity of the thing being described, e.g., "Although other candidates have more experience, he is the people's candidate due to his charisma and ability to relate to the common man."
Could it mean in the case of politics that she's of the people? Or, similar/favorable to her constituency?