The Tet Offensive impacted the United States in the Vietnam War by convincing many Americans that the war was not going to be won and that their government had been lying to them.
By the time of the Tet Offensive in early 1968, the US had been fully engaged in the Vietnam War for more than two years, beginning with the Gulf of Tonkin Resolution in 1964. There had been a hope that the US’s takeover of the war at that point would lead to victory. During those 2 years, the US government constantly reassured Americans that the US was winning the war. By early 1968, the government had been telling the American public that the war was practically over. The government was saying the enemy was on its last legs.
When the Tet Offensive occurred, this was shown to be untrue. It became clear that the enemy was at least strong enough to mount a broad attack on multiple targets. Even though the enemy did not manage to take and hold any of their targets, they still showed they could attack.
When this happened, Americans came to have grave doubts in their government and in the idea that the war could be won. This led to President Johnson’s decision not to run for reelection and to the election of Richard Nixon, who promised to end the war.