How does this tie in with the Cold War?
Nixon had used the Watergate to help make sure he would not lose the presidency election. He had a group of advisors that had been known as "Plumbers". They helped to make sure things could not leak out about him in or more on the pentagon papers. Which five of them has been arrested, which soon they found out that Nixon had been involved the whole scandal. This had soon been known as the Watergate Scandal, Nixon believed he had the right to keep all his conversation and meetings private, so that investigators can not take him public.
How does the World/ U.S. react?
United States: This caused the Americans to be confused, the pentagon papers had already made the U.S. government look bad, so Nixon was up to anything to keep his secrets hidden. So, his lie just made the U.S. people angry, mad, and upset that their trust had been broken.