One of Ms. Weiss’s suggestions was to include an interview with Stephen Miller, a White House deputy chief of staff and the architect of Mr. Trump’s immigration crackdown, or a similarly high-ranking Trump administration official, two of the people said. Ms. Weiss provided contact information for Mr. Miller to the “60 Minutes” staff.

Ms. Weiss also questioned the use of the term “migrants” to describe the Venezuelan men who were deported, noting that they were in the United States illegally, two of the people said.