What happened during 1963-1968 to cause the comeback of the U.S. economy?

Following the 1958 recession, the economy was sluggish at the beginning of John F. Kennedy's presidency (he took office in 1961). Unemployment remained at about 6%, and the stock market had lost a great deal of its value. Worried about the 1964 election, Kennedy decided to drastically lower corporate and personal taxes in 1963 (the bill was signed into law in 1964 after his death), and the economy began to expand on its own. 

After Lyndon Johnson assumed the presidency in 1963 when Kennedy was sadly killed, he declared a War on Poverty that concentrated government resources on reducing poverty. While poverty had fallen from 1947 to 1956, the rate of Americans in poverty, particularly African-Americans, had begun to stagnate. From 1965 to 1968, government spending on the poor doubled, and services such as Head Start, job-training and placement programs, medical care, and Legal Services provided services to the poor in their communities. Johnson also created the health care programs Medicaid and Medicare. These programs provided a safety net for the needy.

In part because of this spending, and in part because of the booming national economy, poverty declined to a great extent during Johnson's presidency. However, after 1968, some of these programs were terminated when Nixon was elected president, while other programs continued. An economic crisis in 1968, partly caused by spending on domestic programs and spending on the Vietnam War, brought an end to the expansion of the United States economy. The costs of the War on Poverty, along with spending on the escalation of the war in Vietnam, were too hard to maintain without increasing taxes, and inflation resulted.