Final answer:
CBS News, particularly through the reporting of Walter Cronkite, played a key role in increasing opposition to the Vietnam War, alongside the publication of the Pentagon Papers by the New York Times.
Step-by-step explanation:
The media outlet that played a significant role in increasing opposition to the war in Vietnam was CBS News. Renowned journalist Walter Cronkite, reporting for CBS News, used the word "stalemate" to describe the Vietnam War after the Tet Offensive in 1968, influencing public opinion. Additionally, the New York Times also had a critical impact when it published the Pentagon Papers in 1971, revealing undisclosed information regarding the true nature of U.S. involvement in Vietnam. This publication helped to sway public opinion by exposing discrepancies between the official government narrative and the realities of wartime decisions and actions.