All the President's Men (1976)

Carl Bernstein: Boy, that woman was paranoid! At one point I - I suddenly wondered how high up this thing goes, and her paranoia finally got to me, and I thought what we had was so hot that any minute CBS or NBC were going to come in through the windows and take the story away.
Bob Woodward: You're both paranoid. She's afraid of John Mitchell, and you're afraid of Walter Cronkite.

Trivia: Frank Wills, the security guard who discovered the Watergate break-in, plays himself.