Mr. Hill, a television journalist who was recently laid off, said in an interview that one of Ms. Trump's lines — the words "strength of your dreams" — caught his attention as he was watching on his computer from a Starbucks in Los Angeles, juggling Facebook chats and browsing Twitter.

Mr. Hill, 31, found the clip of Mrs. Obama's speech online and noticed that parts of the two speeches sounded the same. He then realized that a larger portion appeared to have been borrowed as he continued to examine both.

"I thought, 'That's legit plagiarism,'" said Mr. Hill, who described himself as a supporter of President Obama. "'Someone took this piece and plugged in their own information.'"