What action did President Nixon take that increased opposition to the Vietnam War in the United States?

Answer: Attacking Cambodia.

In 1969, President Nixon authorized bombing raids in Cambodia. Then, beginning in April, 1970, Nixon ordered a ground attack on Vietcong bases in Cambodia.

Pres. Nixon believed attacking in Cambodia was necessary to forestall communist forces from attacking South Vietnam from that direction. But his decision was hugely unpopular with the American public, which did not want further escalation of the war. This was seen as essentially an invasion of Cambodia by the US. A key example of protests were those that occurred at Kent State University in Ohio, in May, 1970, in response to Nixon's Cambodia campaign.