Why did much of the American public and many in the Johnson administration support US escalation in Vietnam?

The US just won WWII! Just won Korea! In both wars with FIREPOWER! Why play games with the commies (was their way of thinking)...use FIREPOWER again and win the darn thing! In either case; President Johnson remembered the atom bomb and the invasion of North Korea which brought in Red China; which escalated the Korean War into a bloody mess. Consequently, cooler heads prevailed...and there would be no nukes in Vietnam nor any invasion of North Vietnam.