I sometimes have difficulty in determining which part of the sentence a prepositional phrase modifies.
1.) I called the man from Hong Kong. <-- Is the pp "from Hong Kong" modifying the object "man" or the verb "called"?
2.) A man of the people from the United States. <-- Is the pp "from the United States" modifying the object of the preposition "people" or the subject "man"?
Let me know if I am missing something here.
"A man of the people" is a common phrase, meaning someone who comes from common roots and/or has the interests of the people at heart. This particular man happens to come from the United States.
Perhaps you wanted to say, instead, that it is a man arising out of "the people of the United States," or "the people of India." That would have a very different meaning. In that case you would have to write the sentence differently so as to avoid confusion, since "man of the people" -- in the sense that I described it -- has become a commonly understood phrase.
So I suppose you could say that "of the United States" is modifying the phrase "man of the people." I prefer to think of it as simply modifying "man."